text:
\section{Introduction}

The development in higher spin (HS) theories shows the importance of dynamics in generalized spaces with supplemented additional tensorial coordinates
 (see e.g. \cite{BL,BLS,BLPS,Vas,PST,BBAST,Vas1}).
In particular, in $D=4$ the massless free HS fields can be derived from the quantization of the spinorial particle model on flat tensorial space, described
by $D=4$ Minkowski space extended by six tensorial coordinates \cite{BL,BLS,Vas} generated by the tensorial central charges. We would like to point out
that six commuting with each other tensorial charges are supplemented as well if we enlarge the Poincare algebra to the Maxwell algebra \cite{Bac,Schr,B,Sor,BG,BGKL}. The
corresponding Maxwell tensorial space-time, generated by fourmomenta and six additional tensorial charges, is endowed in tensorial sector with constant
torsion proportional to  electromagnetic coupling constant $e$. The aim of this paper is to consider the spinorial particle model in ten-dimensional $D=4$
tensorial space-time with torsion described by the coset of $D=4$ Maxwell group. It follows that the additional tensorial coordinates can be linked with
the spin degrees of freedom, and the model after first quantization will describe linear equations for coupled infinite-component HS field multiplets
(Maxwell HS fields).

The Maxwell algebra \cite{Bac,Schr} is obtained as the following enlargement of the Poincare algebra with generators ($P_{\alpha\dot\beta}$,
$M_{\alpha\beta}$, $\bar M_{\dot\alpha\dot\beta}$) by six commuting with each other tensorial charges $Z_{\alpha\beta}=Z_{\beta\alpha}$, $\bar
Z_{\dot\alpha\dot\beta}=(Z_{\alpha\beta})^+$ \footnote{We shall consider in this paper the case $D=4$ and use two-spinor notation, i.e.
$P_{\alpha\dot\beta}=\sigma^{\mu}_{\alpha\dot\beta}P_{\mu}$, $Z_{\alpha\beta}=\sigma^{\mu\nu}_{\alpha\beta}Z_{\mu\nu}$, $\bar
Z_{\dot\alpha\dot\beta}=\tilde\sigma^{\mu\nu}_{\dot\alpha\dot\beta}Z_{\mu\nu}$, where
$(\sigma^\mu)_{\alpha\dot\alpha}=(1_2,\vec{\sigma})_{\alpha\dot\alpha}$,
$(\tilde\sigma^\mu)^{\dot\alpha\alpha}=\epsilon^{\alpha\beta}\epsilon^{\dot\alpha\dot\beta}(\sigma^\mu)_{\beta\dot\beta}=
(1_2,-\vec{\sigma})^{\dot\alpha\alpha}$, $\sigma^{\mu\nu}=i\,\sigma^{[\mu}\tilde\sigma^{\nu]}$, $\tilde\sigma^{\mu\nu}=i\,\tilde\sigma^{[\mu}\sigma^{\nu]}$
$\sigma^{\mu\nu}_{\alpha\beta}=\epsilon_{\beta\gamma}(\sigma^{\mu\nu})_{\alpha}{}^{\gamma}$,
$\tilde\sigma^{\mu\nu}_{\dot\alpha\dot\beta}=\epsilon_{\dot\beta\dot\gamma}(\tilde\sigma^{\mu\nu})^{\dot\gamma}{}_{\dot\alpha}$. Always in this paper we
use weight coefficient in (anti)symmetrization, i.e. $A_{(\alpha}B_{\beta)}=\frac12\,(A_{\alpha}B_{\beta}+A_{\beta}B_{\alpha})$,
$A_{[\alpha}B_{\beta]}=\frac12\,(A_{\alpha}B_{\beta}-A_{\beta}B_{\alpha})$. } \footnote{In (\ref{M-alg}) we do not introduce any dimensionfull parameter,
i.e. we assume that the mass dimension of $Z_{\alpha\beta}$, $\bar Z_{\dot\alpha\dot\beta}$ is 2 (twice of mass dimension of $P_{\alpha\dot\beta}$). We
stress that one can introduce any mass dimensionality $[Z_{\alpha\beta}]=[\bar Z_{\dot\alpha\dot\beta}]$ of tensorial generators by introducing suitable
dimensionfull constant in (\ref{M-alg}). If we assume $[Z_{\alpha\beta}]=[\bar Z_{\dot\alpha\dot\beta}]=1$ we get the case of tensorial coordinates with
dimensionalities as in \cite{BL,BLS,BLPS,Vas,PST,BBAST,Vas1}; if $[Z_{\alpha\beta}]=[\bar Z_{\dot\alpha\dot\beta}]=0$ such form of Maxwell algebra was
considered in \cite{AKLuk,Sor2,Durka}. In Sect.\,1-3 below we shall use only the parameterless form  (\ref{M-alg}-\ref{Lor-alg}) of Maxwell algebra. The
consequences of introducing various dimensionfull parameters in (\ref{M-alg}) for the basic equations derived in this paper we shall consider in Appendix.}
\begin{equation}\label{M-alg} \begin{array}{rrc} &&[P_{\alpha\dot\alpha},P_{\beta\dot\beta}] = 2 i\,e \left(\epsilon_{\dot\alpha\dot\beta}Z_{\alpha\beta}+
\epsilon_{\alpha\beta}\bar Z_{\dot\alpha\dot\beta}\right),\\[7pt] &&[Z_{\alpha\beta},Z_{\gamma\delta}] = [Z_{\alpha\beta},\bar Z_{\dot\alpha\dot\beta}]=
[Z_{\alpha\beta},P_{\gamma\dot\gamma}]=0 \,, \end{array} \end{equation} where \begin{equation}\label{M-alg1} \!\!\!\!\!\!\!\!\!\!\!\!\begin{array}{rrc}
&&[M_{\alpha\beta},P_{\gamma\dot\gamma}] = -i\epsilon_{\gamma(\alpha}P_{\beta)\dot\gamma}\,,\qquad [\bar M_{\dot\alpha\dot\beta},P_{\gamma\dot\gamma}] =
-i\epsilon_{\dot\gamma(\dot\alpha}P_{\gamma\dot\beta)}\,, \\[7pt] &&[M_{\alpha\beta},Z_{\gamma\delta}] = i\left( \epsilon_{\alpha\gamma}Z_{\beta\delta}+
\epsilon_{\beta\delta}Z_{\alpha\gamma}\right), \quad [\bar M_{\dot\alpha\dot\beta},\bar Z_{\dot\gamma\dot\delta}] = i\left(
\epsilon_{\dot\alpha\dot\gamma}\bar Z_{\dot\beta\dot\delta}+ \epsilon_{\dot\beta\dot\delta}\bar Z_{\dot\alpha\dot\gamma}\right), \quad
[M_{\alpha\beta},\bar Z_{\dot\gamma\dot\delta}] = 0 \end{array} \end{equation} and $M_{\alpha\beta}=M_{\beta\alpha}$, $\bar
M_{\dot\alpha\dot\beta}=(M_{\alpha\beta})^+$ describe the Lorentz algebra generators \begin{equation}\label{Lor-alg}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\begin{array}{rrc} &&[M_{\alpha\beta},M_{\gamma\delta}] = i\left( \epsilon_{\alpha\gamma}M_{\beta\delta}+
\epsilon_{\beta\delta}M_{\alpha\gamma}\right), \,\,\,\, [\bar M_{\dot\alpha\dot\beta},\bar Z_{\dot\gamma\dot\delta}] = i\left(
\epsilon_{\dot\alpha\dot\gamma}\bar M_{\dot\beta\dot\delta}+ \epsilon_{\dot\beta\dot\delta}\bar M_{\dot\alpha\dot\gamma}\right), \,\,\,\,
[M_{\alpha\beta},\bar M_{\dot\gamma\dot\delta}] = 0. \end{array} \end{equation} The quantity $e$ in  (\ref{M-alg}) is the dimensionless electromagnetic
coupling constant.

One can introduce Maurer-Cartan (MC) one-forms ($\omega_{(P)}^{\alpha\dot\beta}$, $\omega_{(Z)}^{\alpha\beta}$, $\omega_{(\bar Z)}^{\dot\alpha\dot\beta}$)
on ten-dimensional coset ($\cal{M}$ is the Maxwell group) which defines $D=4$ proper Maxwell group ${\cal{M}}_0$ \begin{equation}\label{M-coset}
{\cal{M}}_0=\frac{\cal{M}}{O(3,1)}=e^{i(z^{\alpha\beta}Z_{\alpha\beta}+\bar z^{\dot\alpha\dot\beta}\bar Z_{\dot\alpha\dot\beta})}
e^{ix^{\alpha\dot\beta}P_{\alpha\dot\beta}}\,. \end{equation} By analogy with the constant torsion in $N=1$ Wess-Zumino superspace, the tensorial Maxwell
space-time described by proper Maxwell group (\ref{M-coset}) is endowed with constant torsion.

The simplest Maxwell generalization of standard relativistic $D=4$ particle model was considered in \cite{FedLuk}, where it was extended to ten-dimensional
tensorial space-time manifold (\ref{M-coset}). It was shown in \cite{FedLuk} that after first quantization such a model presents in Lorentz-covariant way
the $D=4$ particle interacting with electromagnetic (EM) field characterized by a constant field strength (so-called Landau orbit problem). In this paper
we shall generalize the $D=4$ spinorial particle model defined on flat tensorial space-time with supplemented Weyl spinor variable introduced in
\cite{BL,BLS,Vas}. Let us recall that the spinorial massless $D=4$ $N=1$ superparticle model was firstly  described by the following SUSY-invariant action,
proposed by Shirafuji \cite{Shir} \begin{equation}\label{Shir-act} S^{N=1\,SUSY}=\int \,
\lambda_{\alpha}\bar\lambda_{\dot\beta}\,\omega_{(\mathscr{P})}^{\alpha\dot\beta}\,, \end{equation} where the one-form
$\omega_{(\mathscr{P})}^{\alpha\dot\beta}$ is derived from the superalgebra $\{Q_{\alpha},\bar Q_{\dot\beta}\}=2\mathscr{P}_{\alpha\dot\beta}$ and
$\lambda_{\alpha}$, $\bar\lambda_{\dot\alpha}=(\lambda_{\alpha})^+$ is an auxiliary two-component Weyl spinor. Below we shall consider the Maxwell
counterpart of Shirafuji model, which by observing the correspondence $\Big(Q_\alpha, \bar Q_{\dot\beta}; \mathscr{P}_{\alpha\dot\beta} \Big)$
$\leftrightarrow$ $\Big(P_{\alpha\dot\beta}; Z_{\alpha\beta}, \bar Z_{\dot\alpha\dot\beta} \Big)$ and $\omega_{(\mathscr{P})}^{\alpha\dot\beta}$
$\leftrightarrow$ $\Big(\omega_{(Z)}^{\alpha\beta}, \bar\omega_{(\bar Z)}^{\dot\alpha\dot\beta} \Big)$ we define as follows
\begin{equation}\label{Max-act-m} S^{Max} =\int \, \Big( a\lambda_{\alpha}\lambda_{\beta}\omega_{(Z)}^{\alpha\beta} +\bar
a\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\bar\omega_{(\bar Z)}^{\dot\alpha\dot\beta} \Big)\,. \end{equation}

Because the tensorial coordinates $(z^{\alpha\beta},\bar z^{\dot\alpha\dot\beta})$ and one forms $(\omega_{(Z)}^{\alpha\beta},\bar\omega_{(\bar
Z)}^{\dot\alpha\dot\beta})$ have mass dimensionality equal to $-2$ ($[z^{\alpha\beta}]=[\bar z^{\dot\alpha\dot\beta}]=
[\omega_{(Z)}^{\alpha\beta}]=[\bar\omega_{(\bar Z)}^{\dot\alpha\dot\beta}]=-2$; see footnote 2) if as usual we assign
$[\lambda^{\alpha}]=[\bar\lambda^{\dot\alpha}]=\frac12$, we obtain that $[a]=1$. By fixing global $U(1)$ phase transformations
$\lambda_{\alpha}=e^{i\varphi}\lambda_{\alpha}$, $\bar\lambda_{\dot\alpha}=e^{-i\varphi}\bar\lambda_{\dot\alpha}$, which commute with Lorentz
$SL(2;\mathbb{C})$ transformations, the complex parameter $a$ can be made real ($a=\bar a=m$) and introduces in the model a mass-like parameter $m$.

It will be shown (see Sect.\,3) that $m$ is not providing standard notion of mass for particular HS field components; its presence will be seen in the
terms describing couplings between $D=4$ HS fields with different spins. Further, in order to obtain in our model nontrivial ``conformal limit'' $m\to 0$
we shall add to the action (\ref{Max-act-m}) the action (\ref{Shir-act}) with $\mathscr{P}_\mu$ (commuting Poincare momenta) replaced however by the
noncommuting Maxwell momenta $P_\mu$ from (\ref{M-alg}).

In order to perform effectively the quantization which provides the HS field equations in our Maxwell tensorial space $X
=(x^{\alpha\dot\alpha},z^{\alpha\beta}, \bar z^{\dot\alpha\dot\beta} )$ we shall also add to the action  (\ref{Max-act-m}) the free kinetic term linear in
time derivatives of $\lambda_{\alpha}$, $\bar\lambda_{\dot\alpha}$.\footnote{ Such terms in generalized Shirafuji model in $D=4$ tensorial space obtained
by adding to Poincare algebra the tensorial central charges was proposed by Vasiliev \cite{Vas}. }

We recall that the $D=4$ massless conformal fields were obtained as describing first quantization of particle model in flat tensorial space  $X^A
=(x^{\alpha\dot\alpha},z^{\alpha\beta}, \bar z^{\dot\alpha\dot\beta} )$, with additional two-tensor coordinates $z^{\mu\nu}$=($z^{\alpha\beta}$, $\bar
z^{\dot\alpha\dot\beta}$) generated by the tensorial central charges appearing in generalized $D=4$ Poincare superalgebra.\footnote{ Firstly such tensorial
supercharges were postulated in $D=11$ superalgebra what led to the notion of M-algebra \cite{Cur,AzTown,Sezg}. } Further there was considered the
derivation of HS fields in $D=4$ AdS by quantization of the particle model on non-flat tensorial superspace described by the group manifold $Sp(4)$
\cite{BLPS,PST,BBAST}.
In AdS space-time there appears a geometric dimensionfull parameter, AdS radius or cosmological constant, which permits
to introduce interacting higher spin fields for spins $s>2$ \cite{FV87a,FV87b}.
In this paper we introduce other modification of flat tensorial space, characterized by alternative way
of introducing the dimensionfull parameter. In the formulation of Maxwell algebra (\ref{M-alg})
without geometric dimensionfull parameter (see footnote 2)) the mass-like parameter $m$
is dynamical, appears in the action (see (\ref{Maxwell-Lagr})). However one
can change the mass dimensionality of the generators $Z_{\alpha\beta}$, $\bar Z_{\dot\alpha\dot\beta}$ and dual tensorial coordinates
$z^{\alpha\beta}$, $\bar z^{\dot\alpha\dot\beta}$ if we introduce in the relation (\ref{M-alg}) a suitable geometric dimensionfull parameter. In general case one can
replace (\ref{M-alg}) as follows
\begin{equation}\label{M-alg-m}
[P_{\alpha\dot\alpha},P_{\beta\dot\beta}] = 2 i\,eM^{\,\xi}
\left(\epsilon_{\dot\alpha\dot\beta}Z_{\alpha\beta}+ \epsilon_{\alpha\beta}\bar Z_{\dot\alpha\dot\beta}\right)\,,
\end{equation}
where $\xi$ is a real
number, $M$ describes a geometric mass parameter ($[M]=1$), $e$ is dimensionless ($[e]=0$). The value $\xi=0$ was introduced in original Maxwell algebra (\ref{M-alg})
with fourmomenta commutator proportional to dimensionless electromagnetic coupling constant.
If $\xi=1$  the geometric mass-like parameter $M$ enters into the Maxwell algebra,
and one can show that in the dynamical equations of the corresponding particle model the geometric parameter $M$
replaced the dynamical parameter $m$ (see Appendix).
In agreement with the discussion of spin two barrier for higher spin interactions
(see e.g. \cite{BekBS}) we conjecture that it is the presence of new dimensionfull
parameter which permits our framework with coupled higher spin fields.
Because in our model with Maxwell symmetries the particle action contains the
mass parameter $m$,  it implies that the Maxwell-invariant HS dynamics is nonconformal. We shall present below such dynamics, what should help to arrive
at the physical interpretation of additional tensorial coordinates $z^{\alpha\beta}$, $\bar z^{\dot\alpha\dot\beta}$ parametrizing the Maxwell group manifold.

In Sect.\,2 we shall perform the canonical quantization of the model (\ref{Max-act-m}) with supplemented kinetic term for $\lambda^{\alpha}$,
$\bar\lambda^{\dot\alpha}$.\footnote{ The additional kinetic term linear in time derivatives, more proper for spinorial degrees of freedom, was used in
\cite{FZ,Vas,FI}. } By using the phase space formulation we shall specify the set of first and second class constraints. It appears that in first quantized
theory the first class constraints will describe the set of field equations for new higher spin multiplets in the tensorial space $X
=(x^{\alpha\dot\alpha},z^{\alpha\beta}, \bar z^{\dot\alpha\dot\beta} )$ which define new HS Maxwell dynamics. Such equations will describe the
generalization of the known ``unfolded equations'' \cite{BLS,Vas,PST,Vas1} for massless HS free fields with flat space-time derivatives
$\partial_{\alpha\dot\beta}$ replaced by the Maxwell-covariant derivatives $D_{\alpha\dot\beta}$. Important property of our particle model is that the
Casimirs of Maxwell algebra \cite{Schr,Sor} \begin{eqnarray}\label{Max-Cas1} C^{Max}_1 &=& P_{\alpha\dot\beta}P^{\alpha\dot\beta} +4e\Big(M_{\alpha\beta}
Z^{\alpha\beta} +\bar M_{\dot\alpha\dot\beta}\bar Z^{\dot\alpha\dot\beta} \Big)\,, \\[3pt] \label{Max-Cas23} C^{Max}_2 &=& Z_{\alpha\beta} Z^{\alpha\beta}
\,,\qquad\qquad C^{Max}_3 =\bar Z_{\dot\alpha\dot\beta}\bar Z^{\dot\alpha\dot\beta}\,, \\[3pt] \label{Max-Cas4} C^{Max}_4 &=& 2Z^{\alpha\beta}\bar
Z^{\dot\alpha\dot\beta}P_{\alpha\dot\alpha}P_{\beta\dot\beta}  - {\textstyle\frac12}\left(Z^{\gamma\delta}Z_{\gamma\delta}+ \bar
Z^{\dot\gamma\dot\delta}\bar Z_{\dot\gamma\dot\delta}\right) P^{\alpha\dot\alpha}P_{\alpha\dot\alpha}\\ &&\qquad\qquad\qquad\quad\,\,\, +\,
2e\left(Z^{\gamma\delta}Z_{\gamma\delta}- \bar Z^{\dot\gamma\dot\delta}\bar Z_{\dot\gamma\dot\delta}\right) \left(Z^{\alpha\beta}M_{\alpha\beta}- \bar
Z^{\dot\alpha\dot\beta}\bar M_{\dot\alpha\dot\beta}\right)\nonumber \end{eqnarray} will vanish as a consequence of first class constraints. It follows from
(\ref{Max-Cas1}) that for vanishing value of $C^{Max}_1$ the formula for $D=4$ mass square $M^2=\frac12\,P_{\alpha\dot\beta}P^{\alpha\dot\beta}$ is linear
in Lorentz generators describing relativistic angular momenta, what suggests some link with the known mass formulae for Regge trajectories.\footnote{ The
idea of linking $D=2$ Maxwell algebra with Regge trajectories in two-dimensional stringy field theory was firstly suggested by D.\,Soroka and V.\,Soroka
\cite{SS-D}. }

In Sect.\,3 we shall describe the new linear set of field equations for space-time fields describing the infinite-dimensional nonconformal Maxwell-HS
multiplets. Similarly like in SUSY-covariant field theory one uses superspace and the covariant odd derivatives $D_{\alpha}$, $\bar D_{\dot\alpha}$, the
Maxwell-covariant formulation is given by extended tensorial space-time $X=(x_\mu, z_{\mu\nu})$ and Maxwell-covariant space-time derivatives $D_\mu$. If we
expand the fields on Maxwell tensorial space into $D=4$ HS fields with arbitrary Lorentz spins, in comparison with known equations for decoupled free
massless conformal HS fields we obtain the equations with new space-time-dependent terms, which link fields with different values of the Lorentz spins
$(j_1,j_2)$. We shall also show that the second order equations, generalizing the Klein-Gordon equation for the corresponding scalar Maxwell-HS fields can
be described by the bilinear Casimir (\ref{Max-Cas1}) with Maxwell algebra generators $(P_{\alpha\dot\beta},M_{\alpha\beta}, \bar M_{\dot\alpha\dot\beta},
Z_{\alpha\beta},\bar Z_{\dot\alpha\dot\beta} )$ suitably realized in ten-dimensional tensorial space  $X$ describing the generalization of $D=4$
space-time.

We recall that at present there was considered the quantization of spinorial particle model of Shirafuji type on two $D=4$ tensorial manifolds: the flat
one, described by $R^{10}$ \cite{BL,BLS,PST}, and described by the group manifold $Sp(4)$ \cite{BLS,BLPS,Vas,PST,BBAST,Vas1}. Because both tensorial
manifolds can be described by the same coset $Sp(8)/[GL(4)\,{\subset\!\!\!\!\!\!\times} K_{10}]$ ($K_{10}$ is ten-dimensional Abelian group of generalized
conformal translations) \cite{PST}, they provide two different choices of coordinates on the same manifold, and consequently corresponding free particle
models have the same massless spectrum of free conformal HS particles. At present it is not clear if there is a way of ``diagonalizing'' the interacting
Maxwell HS multiplets, and the question of their mass spectrum is the problem for further investigation. Subsequently  at the end of Sect.\,3 we show that
the torsion of Maxwell space-time can be interpreted as describing the coupling to Abelian gauge potential.
Finally in Appendix we shall consider a general scale reparametrization of the
basic algebraic relation (\ref{M-alg}), modifying  the ``canonical'' dimensionality $[Z_{\alpha\beta}]=[\bar Z_{\dot\alpha\dot\beta}]=2$ and introducing
additional, more geometric mass-like parameter $M$.

\setcounter{equation}{0} \section{Maxwell-covariant spinorial particle model and \\ its formulation in generalized phase space}

\subsection{Covariant Maurer-Cartan one-forms}

Taking exponential parametrization (\ref{M-coset}) and using algebraic relations (\ref{M-alg}), (\ref{M-alg1}) we obtain \begin{equation}\label{om-def}
{\cal M}_0^{-1}d {\cal M}_0=i\Big(\omega^{\alpha\dot\beta}P_{\alpha\dot\beta}+\omega^{\alpha\beta}Z_{\alpha\beta} + \bar\omega^{\dot\alpha\dot\beta}\bar Z
_{\dot\alpha\dot\beta} \Big)\,, \end{equation} where the Maurer-Cartan one-forms are \begin{equation}\label{M-om} \begin{array}{ccc}
&&\omega^{\alpha\dot\beta}= d x^{\alpha\dot\beta}\,,\\[5pt] &&\omega^{\alpha\beta}=  d z^{\alpha\beta} + e\,x^{(\alpha\dot\gamma}d
x^{\beta)}_{\dot\gamma}\,,\qquad \bar\omega^{\dot\alpha\dot\beta}= d\bar z^{\dot\alpha\dot\beta}+ e\,x^{\gamma(\dot\alpha}d x^{\dot\beta)}_{\gamma}\,.
\end{array} \end{equation} The dual Maxwell-covariant derivatives $D_A$=($D_{\alpha\dot\beta}$, $D_{\alpha\dot\beta}$, $\bar D_{\dot\alpha\dot\beta}$) are
given by the formulae \begin{equation}\label{M-der} \begin{array}{ccc} && D_{\alpha\dot\beta}= -i\left(\displaystyle\frac{\partial}{\partial
x^{\alpha\dot\beta}} \,\,+ e\,x^{\gamma}_{\dot\beta}\,\displaystyle\frac{\partial}{\partial z^{\alpha\gamma}}\,\,+
e\,x^{\dot\gamma}_{\alpha}\,\displaystyle\frac{\partial}{\partial \bar z^{\dot\beta\dot\gamma}}\right),\\[9pt] && D_{\alpha\beta}=
-i\,\displaystyle\frac{\partial}{\partial z^{\alpha\beta}}\,,\qquad \bar D_{\dot\alpha\dot\beta}= -i\,\displaystyle\frac{\partial}{\partial \bar
z^{\dot\alpha\dot\beta}}\,\,. \end{array} \end{equation} The relations (\ref{M-der}) defines by means of the formula $\left[D_A,D_B\right]=T_{A,B}{}^C D_C$
the nonvanishing torsion in Maxwell tensorial space-time $(x_\mu, z_{\mu\nu})$ \begin{equation}\label{tor}
T_{\mu,\,\nu}{}^{\lambda\rho}=\delta_\mu^{[\lambda} \delta_\nu^{\rho]}\,. \end{equation} The one-forms (\ref{M-om}) and vector fields (\ref{M-der}) are
invariant under the space-time (parameters $a^{\alpha\dot\beta}$) and tensorial Maxwell translations (parameters $b^{\alpha\beta}$, $\bar
b^{\dot\alpha\dot\beta}$) \begin{equation}\label{M-trans} \begin{array}{ccc} &&\delta x^{\alpha\dot\beta}= a^{\alpha\dot\beta}\,,\\[5pt] &&\delta
z^{\alpha\beta}=   b^{\alpha\beta} + x^{(\alpha\dot\gamma}a^{\beta)}_{\dot\gamma}\,,\qquad \delta\bar z^{\dot\alpha\dot\beta}= \bar
b^{\dot\alpha\dot\beta}+ x^{\gamma(\dot\alpha}a^{\dot\beta)}_{\gamma} \end{array} \end{equation} and are covariant under the Lorentz transformations
(parameters $\ell^{\alpha\beta}$, $\bar\ell^{\dot\alpha\dot\beta}$) \begin{equation}\label{M-trans-L} \delta x^{\alpha\dot\beta}=
\ell^{\alpha\gamma}x_{\gamma}^{\dot\beta}+\bar\ell^{\dot\alpha\dot\gamma}x_{\dot\gamma}^{\beta}\,,\qquad \delta z^{\alpha\beta}=
2\ell^{\alpha\gamma}z_{\gamma}^{\beta} \,,\qquad \delta\bar z^{\dot\alpha\dot\beta}= 2\bar\ell^{\dot\alpha\dot\beta}\bar z_{\dot\gamma}^{\dot\beta}\,.
\end{equation}

\subsection{Particle action and constraints}

We shall consider the following Maxwell-invariant particle action
\begin{equation}\label{Maxwell-act}
S=\int \,
\left[\lambda_{\alpha}\bar\lambda_{\dot\beta}\,\omega^{\alpha\dot\beta}+ m\left(\lambda_{\alpha}\lambda_{\beta}\,\omega^{\alpha\beta} +
\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\,\bar\omega^{\dot\alpha\dot\beta}\right) \right]\,.
\end{equation}
{}From action (\ref{Maxwell-act})
follows a complicated structure of the constrains with four first class constraints. Similarly as in the previous HS particle models in tensorial
space-time \cite{BL,BLS}, the appearance of the second class constraints $p_\lambda^{\alpha}\approx0$, $\bar p_\lambda^{\dot\alpha}\approx0$ makes the
quantization difficult. It is useful to convert these constraints into the first class constraints what is achieved by adding four additional degrees of
freedom and new four gauge symmetries \cite{BLS} . Effectively, as shown in \cite{Vas}, such conversion is produced by adding to the action
(\ref{Maxwell-act}) the term with additional coordinates $(y^{\alpha},{\bar y}^{\dot\alpha})$
\begin{equation}\label{Maxwell-act1} S_\lambda=\int d\tau\,
\Big(\lambda_{\alpha}\dot y^{\alpha} + {\bar\lambda}_{\dot\alpha}\dot{\bar y}^{\dot\alpha} \Big)\,. \end{equation} As a result, the constraints
$p_\lambda^{\alpha}\approx0$, $\bar p_\lambda^{\dot\alpha}\approx0$ do not appear and  $y^{\alpha}$, $\bar y^{\dot\alpha}$ play the role of canonical
variables conjugate to $\lambda_{\alpha}$, ${\bar\lambda}_{\dot\alpha}$.

Thus, we consider in this paper the model defined by the Lagrangian
\begin{equation}\label{Maxwell-Lagr}
L=\lambda_{\alpha}\bar\lambda_{\dot\beta}\,\dot
x^{\alpha\dot\beta}+ m\lambda_{\alpha}\lambda_{\beta}\,\Big(\dot z^{\alpha\beta} + e\,x^{\alpha\dot\gamma}\dot x^{\beta}_{\dot\gamma}\Big) +
m\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\,\Big( \dot{\bar z}^{\dot\alpha\dot\beta}+ e\,x^{\gamma\dot\alpha}\dot x^{\dot\beta}_{\gamma} \Big)+
\lambda_{\alpha}\dot y^{\alpha} + {\bar\lambda}_{\dot\alpha}\dot{\bar y}^{\dot\alpha}\,, \end{equation} which describes the particle motion in generalized
coordinate space $(x^{\alpha\dot\beta},z^{\alpha\beta},{\bar z}^{\dot\alpha\dot\beta}, y^{\alpha},\bar y^{\dot\alpha})$. The definitions of corresponding
momenta $(p_{\alpha\dot\beta},f_{\alpha\beta},{\bar f}_{\dot\alpha\dot\beta}, \lambda_{\alpha},\bar\lambda_{\dot\alpha})$ lead to the following constraints
in the model \footnote{ We omit below the consideration of the constraints $p_\lambda^{\alpha}-y^{\alpha}\approx0$, $\bar p_\lambda^{\dot\alpha} -\bar
y^{\dot\alpha}\approx0$ and $p_{y\,\alpha}\approx0$, $\bar p_{y\,\dot\alpha}\approx0$. After introducing for them Dirac brackets the variables
$(\lambda_{\alpha},\bar\lambda_{\dot\alpha})$ become the momenta of $(y^{\alpha},\bar y^{\dot\alpha})$. The tensorial part of the phase space
$(x^{\alpha\dot\beta},z^{\alpha\beta},{\bar z}^{\dot\alpha\dot\beta}, p_{\alpha\dot\beta},f_{\alpha\beta},{\bar f}_{\dot\alpha\dot\beta})$ is supplemented
by auxiliary spinorial phase space $(y^{\alpha},\bar y^{\dot\alpha}, \lambda_{\alpha},\bar\lambda_{\dot\alpha})$ with the canonical Poisson brackets
$\{y^\alpha, \lambda_{\beta}\}_{{}_P}=\delta_{\beta}^\alpha$, $\{\bar y^{\dot\alpha},\bar\lambda_{\dot\beta} \}_{{}_P}=\delta_{\dot\beta}^{\dot\alpha}$.
After quantization these two parts of generalized phase space commute.} \begin{eqnarray}\label{costr-x} T_{\alpha\dot\beta}&\equiv&p_{\alpha\dot\beta}+
e\,f_{\alpha\gamma}x^\gamma_{\dot\beta}+e\,\bar f_{\dot\beta\dot\gamma}x^{\dot\gamma}_{\alpha}-\lambda_{\alpha}\bar\lambda_{\dot\beta}\approx 0\, ,\\[5pt]
T_{\alpha\beta}&\equiv&f_{\alpha\beta}-m\lambda_{\alpha}\lambda_{\beta}\approx 0\,,\label{costr-y}\\[5pt] \bar T_{\dot\alpha\dot\beta}&\equiv&\bar
f_{\dot\alpha\dot\beta}-m\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\approx 0\,.\label{costr-by} \end{eqnarray} It is easy to see that after insertion
of (\ref{costr-y}), (\ref{costr-by}) in (\ref{costr-x}) we obtain the covariantization of the constraints leading to unfolded equations for HS fields
\cite{BLS,Vas} \begin{equation}\label{costr-n} T_{\alpha\dot\beta}= D_{\alpha\dot\beta}-\lambda_{\alpha}\bar\lambda_{\dot\beta}\,, \end{equation} where
\begin{equation}\label{D-cov-cl} D_{\alpha\dot\beta}=p_{\alpha\dot\beta} +e\,x^\gamma_{\dot\beta}p_{\alpha\gamma}+ e\,x^{\dot\gamma}_{\alpha}\bar
p_{\dot\beta\dot\gamma}\,, \end{equation} is the classical counterpart of the Maxwell-covariant derivative.

The only nonvanishing Poisson brackets (PB) of the constraints (\ref{costr-x})-(\ref{costr-by}) are \begin{equation}\label{costr-PB}
\left\{T_{\alpha\dot\alpha}, T_{\beta\dot\beta}\right\}_{{}_P}= 2 e\left(\epsilon_{\dot\alpha\dot\beta} f_{\alpha\beta}+ \epsilon_{\alpha\beta}\bar
f_{\dot\alpha\dot\beta}\right) \approx 2e\, m \left(\epsilon_{\dot\alpha\dot\beta} \lambda_{\alpha}\lambda_{\beta}+
\epsilon_{\alpha\beta}\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\right). \end{equation} Therefore, the constraints (\ref{costr-y}), (\ref{costr-by})
are first class and imply that the tensorial coordinates $(z^{\alpha\beta}, \bar z^{\dot\alpha\dot\beta})$ are becoming pure gauge degrees of freedom
whereas the constraints (\ref{costr-x}) are the superposition of two first class and two second class constraints.

We stress that such structure is not present in the particle model describing the standard free massless HS particles \cite{BLS,Vas}, where the
counterparts of the constraints  (\ref{costr-x}) are first class. Only in limit $e\to 0$ the model  (\ref{Maxwell-Lagr}) yield the standard action
\cite{BLS,Vas} of higher spin particle.

For extracting second class constraints from (\ref{costr-x}) we shall use second Weyl spinor $u_{\alpha}$, as was proposed in \cite{BLS}. Such auxiliary
spinor satisfies the condition $\lambda^\alpha u_{\alpha}=1$ and has nonvanishing PB $\{u_{\alpha},y^\beta \}_{{}_P}=u_{\alpha}u^\beta$ (see details in
\cite{BLS}). Then, considering PB of the projections \begin{equation}\label{costr-pr} T_{\lambda\bar\lambda}\equiv \lambda^\alpha
T_{\alpha\dot\alpha}\bar\lambda^{\dot\alpha}\,, \qquad T_{\lambda\bar u}\equiv \lambda^\alpha T_{\alpha\dot\alpha}\bar u^{\dot\alpha}\,, \qquad
T_{u\bar\lambda}\equiv u^\alpha T_{\alpha\dot\alpha}\bar\lambda^{\dot\alpha}\,, \qquad T_{u\bar u}\equiv u^\alpha T_{\alpha\dot\alpha}\bar
u^{\dot\alpha}\,, \end{equation} we obtain that the unique nonvanishing PB following from (\ref{costr-PB}) is \begin{equation}\label{PB-pr}
\{T_{\lambda\bar u}+T_{u\bar\lambda}, T_{u\bar u}\}_{{}_P}=4e\,m\,. \end{equation} Therefore the constraints ($T_{\lambda\bar u}+T_{u\bar\lambda}$,
$T_{u\bar u}$) are second class constraints, whereas ($T_{\lambda\bar u}-T_{u\bar\lambda}$, $T_{\lambda\bar\lambda}$) are first class.

We introduce now the conversion of the pair of second class constraints into third first class constraint by considering the equation $T_{u\bar u}\approx0$
as gauge fixing condition for the constraint $T_{\lambda\bar u}+T_{u\bar\lambda}\approx0$ generating new gauge degree of freedom. Then, we shall consider
further the constraints (\ref{costr-x}) as described by three first class constraints $T_{\lambda\bar u}\approx0$, $T_{u\bar\lambda}\approx0$,
$T_{\lambda\bar\lambda}\approx0$. Let us observe, however, that these constraints are equivalent to the projections of the constraints  (\ref{costr-x}) on
the Weyl spinor components $\lambda^\alpha$, $\bar\lambda^{\dot\alpha}$. Thus, the equivalent system, which we will quantize, is described by the phase
space variables with nonvanishing PB \begin{equation}\label{PB-c1}
\{x^{\alpha\dot\alpha},p_{\beta\dot\beta}\}_{{}_P}=\delta^{\alpha}_{\beta}\delta^{\dot\alpha}_{\dot\beta},\qquad
\{z^{\alpha\beta},f_{\gamma\delta}\}_{{}_P}=\delta^{(\alpha}_{\gamma}\delta^{\beta)}_{\delta},\qquad \{\bar z^{\dot\alpha\dot\beta},\bar
f_{\dot\gamma\dot\delta}\}_{{}_P}=\delta^{(\dot\alpha}_{\dot\gamma}\delta^{\dot\beta)}_{\dot\delta}, \end{equation} \begin{equation}\label{PB-c2}
\{y^\alpha, \lambda_{\beta}\}_{{}_P}=\delta_{\beta}^\alpha, \qquad \{\bar y^{\dot\alpha},\bar\lambda_{\dot\beta} \}_{{}_P}=\delta_{\dot\beta}^{\dot\alpha}
\end{equation} and the following first class constraints \begin{eqnarray}\label{costr-x1}
S_{\alpha}&\equiv&T_{\alpha\dot\beta}\bar\lambda^{\dot\beta}=\left( p_{\alpha\dot\beta}+ e\,f_{\alpha\gamma}x^{\gamma}_{\dot\beta}
\right)\bar\lambda^{\dot\beta} \approx D_{\alpha\dot\beta}\bar\lambda^{\dot\beta}\approx 0\, ,\\[5pt] \label{costr-x1a} \bar
S_{\dot\alpha}&\equiv&\lambda^{\beta}T_{\beta\dot\alpha}=\lambda^{\beta}\left( p_{\beta\dot\alpha}+ e\,\bar f_{\dot\alpha\dot\gamma}
x_{\beta}^{\dot\gamma}\right) \approx \lambda^{\beta} D_{\beta\dot\alpha}\approx 0\, ,\\[5pt]
T_{\alpha\beta}&\equiv&f_{\alpha\beta}-m\lambda_{\alpha}\lambda_{\beta}\approx 0\,,\label{costr-y1}\\[5pt] \bar T_{\dot\alpha\dot\beta}&\equiv&\bar
f_{\dot\alpha\dot\beta}-m\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\approx 0\,.\label{costr-by1} \end{eqnarray} Because \begin{equation}
\lambda^{\alpha}S_{\alpha}\approx\bar\lambda^{\dot\alpha}\bar S_{\dot\alpha} \end{equation} the four relations (\ref{costr-x1}), (\ref{costr-x1a}) describe
only three independent first class constraints.

It is useful to make some comment about projections in (\ref{costr-x1}), (\ref{costr-x1a}). By performing these projections we omit the contribution in
first class constraints which does not depend on spinor variables and describes the field equation for spin zero case. Such contribution is present in the
following quadratic first class constraint \begin{equation}\label{constr-x3} T\equiv T_{\alpha\dot\beta}T^{\alpha\dot\beta}\approx 0\,. \end{equation}
Indeed, using $\lambda^\alpha u_\alpha=\bar\lambda^{\dot\alpha} \bar u_{\dot\alpha}=1$ we obtain $T=T_{\lambda\bar\lambda}T_{u\bar u}-T_{\lambda\bar
u}T_{u\bar\lambda}\approx 0$ because after conversion the constraints $T_{\lambda\bar u}\approx0$, $T_{u\bar\lambda}\approx0$,
$T_{\lambda\bar\lambda}\approx0$ are of first class. We add that the constraint (\ref{constr-x3}) will provide the Maxwell extension of massless
Klein-Gordon (KG) equation satisfied by the free conformal HS fields.

\subsection{Noether charges and the Casimirs}

In order to interprete the role of the first class constraints (\ref{costr-x1})-(\ref{costr-by1}), (\ref{constr-x3}) in our model we will find the Noether
currents, generated by the Maxwell generators $(P_{\alpha\dot\beta},Z_{\alpha\beta},\bar Z_{\dot\alpha\dot\beta},M_{\alpha\beta},\bar
M_{\dot\alpha\dot\beta})$ in generalized coordinate space $(x^{\alpha\dot\beta},z^{\alpha\beta},\bar z^{\dot\alpha\dot\beta}, y^{\alpha},\bar
y^{\dot\alpha})$. Using the transformations (\ref{M-trans}), (\ref{M-trans-L}) and~\footnote{The spinors $\lambda_\alpha$, $y^{\alpha}$ are inert with
respect to space-time and Maxwell translations.} \begin{equation}\label{M-trans-L1} \delta y^{\alpha}=  \ell^{\alpha\beta}y_{\beta} \,,\quad \delta\bar
y^{\dot\alpha}= \bar\ell^{\dot\alpha\dot\beta}\bar y_{\dot\beta}\,,\qquad \delta \lambda_{\alpha}=  -\ell_{\alpha\beta}\lambda^{\beta} \,,\quad \delta\bar
\lambda_{\dot\alpha}= -\bar\ell_{\dot\alpha\dot\beta}\bar\lambda^{\dot\beta} \end{equation} we obtain the following dynamical phase space realization of
Maxwell algebra generators \begin{equation}\label{M-gen-cl} \begin{array}{rcl} P_{\alpha\dot\beta}&=&-p_{\alpha\dot\beta}+e\,x_{\alpha}^{\dot\gamma}\bar
f_{\dot\gamma\dot\beta}+e\,f_{\alpha\gamma} x_{\dot\beta}^{\gamma}\,,\\[5pt] Z_{\alpha\beta}&=&-f_{\alpha\beta}\,,\qquad \qquad \bar
Z_{\dot\alpha\dot\beta}\,\,\,=\,\,\,-\bar f_{\dot\alpha\dot\beta}\,,\\[5pt] M_{\alpha\beta}&=&x_{(\alpha}^{\dot\gamma}p_{\beta)\dot\gamma} +
2z_{(\alpha}^{\gamma}f_{\beta)\gamma} +y_{(\alpha}\lambda_{\beta)}\,,\\[5pt] \bar M_{\dot\alpha\dot\beta}&=&x_{(\dot\alpha}^{\gamma}p_{\gamma\dot\beta)} +
2\bar z_{(\dot\alpha}^{\dot\gamma}\bar f_{\dot\beta)\dot\gamma} +\bar y_{(\dot\alpha}\bar \lambda_{\dot\beta)}\,. \end{array} \end{equation}

Using the expressions (\ref{M-gen-cl}) we find that the Casimirs (\ref{Max-Cas1}), (\ref{Max-Cas23}), (\ref{Max-Cas4}) of Maxwell algebra are expressed as
follows in terms of the first class constraints
 (\ref{costr-x1})-(\ref{costr-y1}), (\ref{constr-x3}):
\begin{equation}\label{Cas-fix} \begin{array}{rcl} C^{Max}_1 &\approx&T_{\alpha\dot\beta} T^{\alpha\dot\beta}+2\lambda^\alpha S_\alpha\,,\\[5pt] C^{Max}_2
&\approx&T_{\alpha\beta} T^{\alpha\beta} \,,\qquad\qquad C^{Max}_3 \approx\bar T_{\dot\alpha\dot\beta}\bar T^{\dot\alpha\dot\beta}\,,\\[5pt] C^{Max}_4
&\approx&2\lambda^\alpha \bar \lambda^{\dot\alpha} S_\alpha \bar S_{\dot\alpha}\,. \end{array} \end{equation} The numerical eigenvalues of Casimirs
(\ref{Cas-fix}) characterize the choice of infinite-dimensional Maxwell-HS irreducible field multiplets. It appears from the quantization of our
Maxwell-Shirafuji model that we obtain the Maxwell-HS realizations corresponding to all four eigenvalues of Casimirs (\ref{Cas-fix}) equal to zero.

\setcounter{equation}{0} \section{First quantization of the particle model and  interacting HS fields}

\subsection{HS field equations from first class constraints}

We consider the Schr\"{o}dinger representation in which the wave function depends on the generalized coordinates \begin{equation}\label{WF-a} \Phi
=\Phi(x^{\alpha\dot\beta},z^{\alpha\beta}, \bar z^{\dot\alpha\dot\beta}, y^\alpha,\bar y^{\dot\alpha}) \end{equation} and the generalized quantized momenta
are realized by the partial derivatives \begin{equation}\label{op-real1-a} p_{\alpha\dot\beta}=-i\frac{\partial\,\,}{\partial x^{\alpha\dot\beta}}\equiv
-i\partial_{\alpha\dot\beta}\,,\qquad f_{\alpha\beta}=-i\frac{\partial\,\,}{\partial z^{\alpha\beta}}\equiv -i\partial_{\alpha\beta}\,,\qquad \bar
f_{\dot\alpha\dot\beta}=-i\frac{\partial\,\,}{\partial \bar z^{\dot\alpha\dot\beta}}\equiv -i\bar\partial_{\dot\alpha\dot\beta}\,, \end{equation}
\begin{equation}\label{op-real2-a} \lambda_{\alpha}=-i\frac{\partial\,\,}{\partial y^{\alpha}}\equiv  -i\partial_{\alpha}\,,\qquad
\bar\lambda_{\dot\alpha}=-i\frac{\partial\,\,}{\partial \bar y^{\dot\alpha}}\equiv  -i\bar\partial_{\dot\alpha}\,. \end{equation} The Maxwell-covariant
momenta $D_{\alpha\dot\beta}$ (see (\ref{D-cov-cl})) after quantization satisfy the relation \begin{equation}\label{d-costr-com-a}
\left[D_{\alpha\dot\alpha}, D_{\beta\dot\beta}\right]= 2i\,e \left(\epsilon_{\dot\alpha\dot\beta} f_{\alpha\beta}+ \epsilon_{\alpha\beta}\bar
f_{\dot\alpha\dot\beta}\right) \end{equation} and in Schr\"{o}dinger realization describe the Maxwell-covariant derivative. Physical field equations are
defined by the quantum counterpart of first class constraints  (\ref{costr-x1})-(\ref{costr-y1}): \begin{eqnarray}\label{q-costr-x1-a} i
D_{\alpha\dot\beta}\bar\partial^{\dot\beta}\,\Phi&=&\left(\partial_{\alpha\dot\beta}+
e\,\partial_{\alpha\gamma}\,x_{\dot\beta}^{\gamma}\right)\bar\partial^{\dot\beta}\,\Phi= 0\, ,\\[5pt] \label{q-costr-z1-a} i
D_{\beta\dot\alpha}\partial^{\beta}\,\Phi&=&\left(\partial_{\beta\dot\alpha}+ e\,\bar \partial_{\dot\alpha\dot\gamma} \,x_{\beta}^{\dot\gamma}
\right)\partial^{\beta}\, \Phi= 0\, , \end{eqnarray} \begin{equation}\label{q-costr-y1-a} \Big(\partial_{\alpha\beta}+ i m\partial_{\alpha}
\partial_{\beta}\Big)\Phi=0\,,\qquad\qquad \Big(\bar \partial_{\dot\alpha\dot\beta}+ im \bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\Big)\Phi=0\,.
\end{equation}

Let us use the Taylor expansion of the wave function $\Phi$ with respect to the variables $z\equiv z^{\alpha\beta}$ and $\bar z\equiv \bar
z^{\dot\alpha\dot\beta}$. Then the constraints (\ref{q-costr-y1-a}) for the wave function \begin{equation}\label{WF-1-a} \Phi(x,z, \bar z, y,\bar y)=
\sum_{k,n=0}^{\infty}\frac{1}{k!n!}\,z^{\alpha_1\beta_1}...z^{\alpha_k\beta_k}\, \bar z^{\dot\alpha_1\dot\beta_1}...\bar z^{\dot\alpha_n\dot\beta_n}
\,\Phi^{(2k,2n)}_{\alpha_1\beta_1...\alpha_k\beta_k\,\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n}(x,y,\bar y) \end{equation} provide the expression
of all components $\Phi^{(k,n)}$, $k>0$, $n>0$ by $\Phi^{(0,0)}$ as follows: \begin{equation}\label{WF-1-comp-a}
\Phi^{(2k,2n)}_{\alpha_1\beta_1...\alpha_k\beta_k\,\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n}(x,y,\bar y)= (-im)^{k+n}\,\partial_{\alpha_1}
\partial_{\beta_1}\,...\, \partial_{\alpha_k} \partial_{\beta_k}\,\, \bar\partial_{\dot\alpha_1}\bar\partial_{\dot\beta_1}\,...\,
\bar\partial_{\dot\alpha_n}\bar\partial_{\dot\beta_n}\, \,\Phi^{(0,0)}(x,y,\bar y)\,. \end{equation} The formulae (\ref{WF-1-comp-a}) can be written down
as the solutions of eqs.\,(\ref{q-costr-y1-a}) by one compact formula \begin{equation}\label{WF-1-comp1} \Phi(x,z, \bar z, y,\bar
y)=e^{-im\left(z^{\alpha\beta}\partial_{\alpha} \partial_{\beta}+\bar z^{\dot\alpha\dot\beta}\bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\right)}
\Phi^{(0,0)}(x, y,\bar y)\,, \end{equation} what confirms the auxiliary gauge nature of the tensorial coordinates $z^{\mu\nu}=(z^{\alpha\beta},\bar
z^{\dot\alpha\dot\beta})$.

Let us analyze the remaining equations (\ref{q-costr-x1-a}), (\ref{q-costr-z1-a}) for the unique unconstrained component $\Phi^{(0,0)}(x, y,\bar y)$ of the
wave function  (\ref{WF-1-a}). We perform the following subsequent Taylor expansion \begin{equation}\label{WF-0-a} \Phi^{(0,0)}(x, y,\bar y)=
\sum_{k,n=0}^{\infty} \frac{1}{k!n!}\, y^{\alpha_1}...y^{\alpha_k}\, \bar y^{\dot\beta_1}...\bar y^{\dot\beta_n}
\,\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)\,, \end{equation} where
$\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)$ are the $D=4$ space-time Maxwell-HS fields.

Note, that in limit $e\to 0 $ the equations (\ref{q-costr-x1-a}), (\ref{q-costr-z1-a}) yield massless Dirac-Pauli-Fierz equations for massless conformal HS
fields with arbitrary helicity
\begin{equation}\label{Dir-m0-a}
e=0\,:\qquad\qquad
\partial^{\alpha_1\dot\gamma}\,\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)=0\,,\qquad
\partial^{\gamma\dot\beta_1}\,\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)=0\,.
\end{equation}
If $e\neq 0 $ we obtain the
generalization of these equations.

Now we list the equations for Maxwell-HS fields which are the consequence of (\ref{q-costr-x1-a}), (\ref{q-costr-z1-a}): \begin{itemize} \item Using
two-spinor identities $\partial^{\alpha}\partial_{\alpha}=\bar\partial^{\dot\alpha}\bar\partial_{\dot\alpha}=0$ we obtain the equation
\begin{equation}\label{Tr-Psi-a} \partial^{\alpha\dot\alpha}\partial_{\alpha}\bar\partial_{\dot\alpha}\,\Phi=0 \end{equation} which gives the generalized
Lorentz divergence conditions for the component fields in (\ref{WF-0-a}) \begin{equation}\label{Tr-comp-a}
\partial^{\alpha_1\dot\beta_1}\,\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)=0\,,\qquad k,n\geq 1\,. \end{equation} For $n=k=1$ we
obtain the standard Lorentz condition for the four-vector field. \item We obtain also the equations \begin{equation}\label{Eq-Psi-a}
\partial_{\dot\alpha}^{\beta}\,\partial_{\alpha}\partial_{\beta}\,\Phi=
\partial^{\dot\beta}_{\alpha}\,\bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\,\Phi \end{equation} which lead to the following set of equations
\begin{equation}\label{Eq-comp-a} \partial_{\dot\beta_{n-1}}^{\,\alpha_k}\,\phi^{(k,n-2)}_{\alpha_1...\alpha_{k-1}\alpha_k\,\dot\beta_1...\dot\beta_{n-2}}=
\partial^{\,\dot\beta_n}_{\alpha_{k-1}}\,\phi^{(k-2,n)}_{\alpha_1...\alpha_{k-2}\,\dot\beta_1...\dot\beta_{n-1}\dot\beta_n} \,,\qquad k,n\geq 2\,.
\end{equation} for the component fields. In particular for antisymmetric 2-tensors described by Lorentz spins $(2,0)+(0,2)$ we have the following equation
\begin{equation}\label{Eq-comp-M-a} \partial_{\dot\alpha}^{\,\beta}\,\phi^{(2,0)}_{\alpha\beta}=
\partial^{\,\dot\beta}_{\alpha}\,\phi^{(0,2)}_{\dot\alpha\dot\beta}\,. \end{equation} \item After inserting of (\ref{WF-0-a}) the equations
(\ref{q-costr-x1-a}), (\ref{q-costr-z1-a}) produce the following equations for component fields \begin{equation}\label{Eq-Dir-comp1-a}
\partial_{\dot\beta_{n+1}}^{\,\alpha_k}\,\phi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_{n}}=
iem\,x^{\,\alpha_k\dot\beta_{n+2}}\,\phi^{(k,n+2)}_{\alpha_1...\alpha_{k}\,\dot\beta_1...\dot\beta_{n+1}\dot\beta_{n+2}} \,,\qquad k\geq 1\,;
\end{equation} \begin{equation}\label{Eq-Dir-comp2-a}
\partial^{\,\dot\beta_n}_{\alpha_{k+1}}\,\phi^{(k,n)}_{\alpha_1...\alpha_{k}\,\dot\beta_1...\dot\beta_n}=
iem\,x^{\alpha_{k+2}\dot\beta_{n}}\,\phi^{(k+2,n)}_{\alpha_1...\alpha_{k+1}\alpha_{k+2}\,\dot\beta_1...\dot\beta_{n}} \,,\qquad n\geq 1\,, \end{equation}
which are the Maxwell-invariant generalizations of Dirac-Pauli-Fierz equations. \item The last constraint  (\ref{constr-x3}) takes in first-quantized
theory the following form \begin{equation}\label{q-constr-x3-a}
\left[-\partial_{\alpha\dot\alpha}\partial^{\alpha\dot\alpha}-2i\partial^{\alpha\dot\alpha}\partial_{\alpha}\bar\partial_{\dot\alpha}+ 2iem
\left(x^{\beta}_{\dot\alpha}\,\partial^{\alpha\dot\alpha}\partial_{\alpha}\partial_{\beta}+
x_{\alpha}^{\dot\beta}\,\partial^{\alpha\dot\alpha}\bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\right)
-2e^2m^2\left(\partial_{\alpha}x^{\alpha\dot\alpha}\bar\partial_{\dot\alpha}\right)^2\,\right]\Phi= 0\,. \end{equation} However, from
(\ref{q-costr-x1-a}), (\ref{q-costr-z1-a}) and  (\ref{Eq-Psi-a}) follows the equations \begin{equation}\label{eq-constr-dop-a}
ix^{\beta}_{\dot\alpha}\,\partial^{\alpha\dot\alpha}\partial_{\alpha}\partial_{\beta}\,\Phi=
ix_{\alpha}^{\dot\beta}\,\partial^{\alpha\dot\alpha}\bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\,\Phi=
em\,\left(\partial_{\alpha}x^{\alpha\dot\alpha}\bar\partial_{\dot\alpha}\right)^2\,\Phi\,. \end{equation} Using the relations (\ref{eq-constr-dop-a}) and
(\ref{Tr-Psi-a}) we can reduce the constraint (\ref{q-constr-x3-a}) to the following form \begin{equation}\label{q-constr-x3-Psi-a}
\left[-\partial_{\alpha\dot\alpha}\partial^{\alpha\dot\alpha}
+2e^2m^2\left(\partial_{\alpha}x^{\alpha\dot\alpha}\bar\partial_{\dot\alpha}\right)^2\,\right]\Phi= 0\,. \end{equation} The equation
(\ref{q-constr-x3-Psi-a}) provides the following infinite set of component field equations \begin{equation}\label{Eq-KG-comp-a}
\partial^{\gamma\dot\gamma}\partial_{\gamma\dot\gamma}\,\phi^{(k,n)}_{\alpha_1...\alpha_{k}\,\dot\beta_1...\dot\beta_n}=
2e^2m^2\,x^{\alpha_{k+1}\dot\beta_{n+1}}\,x^{\alpha_{k+2}\dot\beta_{n+2}}\,
\phi^{(k+2,n+2)}_{\alpha_1...\alpha_{k}\alpha_{k+1}\alpha_{k+2}\,\dot\beta_1...\dot\beta_{n}\dot\beta_{n+1}\dot\beta_{n+2}} \,, \end{equation} which are
Maxwell-invariant generalization of massless Klein-Gordon equations. One can demonstrate that the Maxwell-Klein-Gordon equations (\ref{Eq-KG-comp-a}) for
all component fields $\phi^{(k,n)}$, except $\phi^{(0,0)}$, can be derived from the Maxwell-Dirac equations (\ref{Eq-Dir-comp1-a}), (\ref{Eq-Dir-comp2-a}).
Single additional equation for the component fields following from  (\ref{Eq-KG-comp-a}) is the Maxwell-Klein-Gordon equation for the scalar field
$\phi^{(0,0)}$: \begin{equation}\label{Eq-KG-comp-0-a} \partial^{\gamma\dot\gamma}\partial_{\gamma\dot\gamma}\,\phi^{(0,0)}=
2e^2m^2\,x^{\alpha_{1}\dot\beta_{1}}\,x^{\alpha_{2}\dot\beta_{2}}\, \phi^{(2,2)}_{\alpha_1\alpha_{2}\,\dot\beta_1\dot\beta_{2}} \,. \end{equation}
\end{itemize}

In order to specify in our model the irreducible Maxwell-HS multiplets let us represent down the Maxwell algebra generators  (\ref{M-gen-cl}) in terms of
realizations (\ref{op-real1-a}), (\ref{op-real2-a}). We obtain that the infinitesimal Maxwell symmetry transformations are the following
\begin{equation}\label{M-gen-qu-a} \begin{array}{rcl} P_{\alpha\dot\beta}&:\quad&\delta_P\phi^{(k,n)}_{\,\cdots}=
a^{\gamma\dot\gamma}\partial_{\gamma\dot\gamma}\phi^{(k,n)}_{\,\cdots}+
iem\,a^{\alpha\dot\gamma}\partial^{\beta}_{\dot\gamma}\phi^{(k+2,n)}_{\,\alpha\beta\,\cdots} +
iem\,a^{\dot\alpha\gamma}\partial^{\dot\beta}_{\gamma}\phi^{(k,n+2)}_{\,\cdots\, \dot\alpha\dot\beta}\,,\\[5pt]
Z_{\alpha\beta}&:\quad&\delta_Z\phi^{(k,n)}_{\,\cdots}= -i em\,b^{\alpha\beta}\phi^{(k+2,n)}_{\,\alpha\beta\,\cdots} \,,\\[5pt] \bar
Z_{\dot\alpha\dot\beta}&:\quad&\delta_{\bar Z}\phi^{(k,n)}_{\,\cdots}= -i em\,\bar b^{\dot\alpha\dot\beta}\phi^{(k,n+2)}_{\,\cdots\,
\dot\alpha\dot\beta}\,,\\[5pt] M_{\alpha\beta},\bar M_{\dot\alpha\dot\beta}&:\quad&\delta_M\phi^{(k,n)}_{\,\alpha\,\cdots\,\dot\alpha}=
-\left(\ell^{\beta\gamma}x^{\dot\gamma}_{\beta}+
\bar\ell^{\dot\beta\dot\gamma}x^{\gamma}_{\dot\beta}\right)\partial_{\gamma\dot\gamma}\phi^{(k,n)}_{\,\alpha\,\cdots\,\dot\alpha}+ k\,
\ell^{\beta}_{\alpha}\phi^{(k,n)}_{\,\beta\,\cdots\,\dot\alpha} + n\, \bar\ell^{\dot\beta}_{\dot\alpha}\phi^{(k,n)}_{\,\alpha\,\cdots\,\dot\beta}\,.
\end{array} \end{equation}

From the relations  (\ref{M-gen-qu-a}) follows that one can construct the infinite-dimensional Maxwell-HS multiplets with minimal Lorentz spin
$(\frac{k}{2},\frac{n}{2})$ described by the field $\phi^{(k,n)}(x)$ if we supplement the infinite chain of component fields $\phi^{(k+2p,n+2r)}(x)$ where
$p=0,1,2,...$, $r=0,1,2,...$. One can observe that \begin{description} \item[i)] There are two infinite sets (bosonic and fermionic) of
infinite-dimensional fields: with integer spins $s=\frac{1}{2}(k+n)+p+r$ ($k+n$ even) and with half-integer spins ($k+n$ odd). \item[ii)] The field
equations relating the components $\phi^{(k+2p,n+2r)}(x)$ are given by the Maxwell-Weyl equations (\ref{Eq-Dir-comp1-a}), (\ref{Eq-Dir-comp2-a}) and
supplementary equations (\ref{Eq-comp-a}); only for spin-zero field $\phi^{(0,0)}$ we should supplement the Maxwell-Klein-Gordon equations
(\ref{Eq-KG-comp-0-a}). In particular, the maximal bosonic Maxwell HS multiplet with scalar field $\phi^{(0,0)}(x)$ will contain the link between all
components with even Lorents spins $(j_1,j_2)=(p,r)$, and there are two maximal fermionic multiplets: chiral, with Maxwell-Weyl field
$\phi^{(1,0)}_{\alpha}(x)$, and the antichiral one , with Maxwell-Weyl field $\phi^{(0,1)}_{\dot\alpha}(x)$ (in Majorana case they are related by the
relation $\phi^{(0,1)}_{\dot\alpha}(x)=(\phi^{(1,0)}_{\alpha}(x))^\dagger$). \item[iii)] The equations (\ref{Eq-comp-a}), (\ref{Eq-Dir-comp1-a}) and
(\ref{Eq-Dir-comp2-a}) link the fields with different spins $(k,n)$. For $k\geq 1$ and $n\geq 1$ the table of fields $\phi^{(k,n)}(x)$ can be decomposed
into triplet of spins with the closed diagram \begin{equation}\label{d-close} (k,n) \quad \stackrel{(3.18)}{\dashleftarrow\dashrightarrow} \quad (k,n+2)
\quad \stackrel{(3.16)}{\dashleftarrow\dashrightarrow} \quad  (k+2,n) \quad \stackrel{(3.19)}{\dashleftarrow\dashrightarrow} \quad  (k,n) \end{equation}
where over the double arrows we indicate the field equation which connects different spins. For the fields with spins $(k,0)$ and $(0,n)$ one can not
construct closed sequence of links, however one can relate all the bosonic ($k+n$ even) or fermionic ($k+n$ odd) fields of a such type (they correspond to
self-dual curvatures of higher spin gauge fields). One can compose the following two sequences \begin{equation}\label{d-unclose} \begin{array}{lll} &&
(k,0) \quad \stackrel{(3.18)}{\dashleftarrow\dashrightarrow} \quad (k,2) \quad \stackrel{(3.16)}{\dashleftarrow\dashrightarrow} \quad  (k+2,0)  \\[5pt] &&
(0,n) \quad \stackrel{(3.19)}{\dashleftarrow\dashrightarrow} \quad (2,n) \quad \stackrel{(3.16)}{\dashleftarrow\dashrightarrow} \quad  (0,n+2) \end{array}
\end{equation} \end{description}

We stress that the coupling between different spins described in (\ref{d-close}), (\ref{d-unclose}) by double arrows is
proportional to $em$. In particular if $e\to 0$ the fields with different spins are decoupled, and the equations (\ref{Eq-Dir-comp1-a}),
(\ref{Eq-Dir-comp2-a}) describe the Dirac-Pauli-Fierz equations (\ref{Dir-m0-a}) for free HS fields; the limit $e\to 0$ of  (\ref{Eq-KG-comp-0-a}) describes free
Klein-Gordon equation for spinless field.

We emphasize that performing the limit $e\to 0 $ on the level of the action with Lagrangian (\ref{Maxwell-Lagr})
and subsequent quantization provides only subset of free fields described by equations (\ref{Dir-m0-a}).
In such free HS model the spectrum contains only the scalar field $\phi^{(0,0)}(x)$,
the spin-tensor fields with undotted indices $\phi^{(k,0)}_{\alpha_1...\alpha_k}(x)$ ($k>0$) and spin-tensor field
with dotted indices $\phi^{(0,n)}_{\dot\alpha_1...\dot\alpha_n}(x)$ ($n>0$).
This is due to the property of the action (\ref{Maxwell-Lagr}) in the limit $e\to 0 $, in which all ten constraints in the system become of the first class,
in particular all the constraints (\ref{costr-x}). Corresponding unfolded equations
$\left( \partial_{\alpha\dot\beta}+ i  \partial_{\alpha}\bar\partial_{\dot\beta}\right)\Phi=0$ yield besides the equations
(\ref{Dir-m0-a}) and the Klein-Gordon equation for scalar field $\phi^{(0,0)}(x)$ also the constraints which express `mixed' fields
$\phi^{(k>0,n>0)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x)$ in terms of space-time
derivatives of the fields $\phi^{(0,0)}(x)$, $\phi^{(k>0,0)}_{\alpha_1...\alpha_k}(x)$, $\phi^{(0,n>0)}_{\dot\alpha_1...\dot\alpha_n}(x)$
(see details in \cite{BLS,Vas}).

If $e\neq 0$ it was shown in Sect.\,3.1 that only eight out of ten constraints (\ref{costr-x})-(\ref{costr-by})
are first class and one can introduce the fields $\phi^{(k,n)}$ for $k\neq 0$, $n\neq 0$ as independent.
Such fields enter together with the ``unfolded'' field $\phi^{(k,0)}_{\alpha_1...\alpha_k}(x)$ into
the infinite-dimensional multiplet $\phi^{(k+2p,2r)}$ which describes an infinite-dimensional realization
(see (\ref{M-gen-qu-a})) of $D=4$ Maxwell algebra.

Finally we add that the appearance of multiplicative massive parameter $m$ can not be avoided; it could be traced to nonvanishing
dimensionalities of fourmomenta $P_\mu$ and the space-time coordinates. In principle one can only rearrange the dimensionality $[Z_{\mu\nu}]$ of the
generators $Z_{\mu\nu}$, but as we show in the Appendix, if we consistently remove $m$ in the Lagrangian (\ref{Maxwell-Lagr}) by assuming that
$[Z_{\mu\nu}]=1$, we will be forced to introduce massive parameter $M$ into the Maxwell algebra relations (\ref{M-alg}) as well as in Maurer-Cartan one
forms (\ref{M-om}).

\subsection{HS field equations in dual picture for tensorial coordinates}

We can also consider the Schr\"{o}dinger representation in which the wave function is related by Fourier transform in the tensorial sector
\begin{equation}\label{WF} \tilde\Psi =\tilde\Psi(x^{\alpha\dot\beta},f_{\alpha\beta}, \bar f_{\dot\alpha\dot\beta}, y^\alpha,\bar y^{\dot\alpha})\,.
\end{equation} The generalized dual momenta variables are realized by the following partial derivatives \begin{equation}\label{op-real1}
z^{\alpha\beta}=i\frac{\partial\,\,}{\partial f_{\alpha\beta}}\,,\qquad \bar z^{\dot\alpha\dot\beta}=i\frac{\partial\,\,}{\partial \bar
f_{\dot\alpha\dot\beta}}\,. \end{equation} The Maxwell-covariant quantum momenta $D_{\alpha\dot\beta}$ satisfy the relation
\begin{equation}\label{d-costr-com} \left[D_{\alpha\dot\alpha}, D_{\beta\dot\beta}\right]= 2i\,e \left(\epsilon_{\dot\alpha\dot\beta} f_{\alpha\beta}+
\epsilon_{\alpha\beta}\bar f_{\dot\alpha\dot\beta}\right) \end{equation} and describe the Maxwell-covariant derivative in Schr\"{o}dinger realization
(\ref{op-real1}). The field equations are defined by the quantum counterpart of first class constraints  (\ref{costr-x1})-(\ref{costr-y1}):
\begin{eqnarray}\label{q-costr-x1} i D_{\alpha\dot\beta}\bar\partial^{\dot\beta}\,\tilde\Psi&=&\left(\partial_{\alpha\dot\beta}+ i
\,e\,f_{\alpha\gamma}\,x_{\dot\beta}^{\gamma}\right)\bar\partial^{\dot\beta}\,\tilde\Psi= 0\, ,\\[5pt] \label{q-costr-x1a} i
D_{\beta\dot\alpha}\partial^{\beta}\,\tilde\Psi&=&\left(\partial_{\beta\dot\alpha}+ i \,e\,\bar f_{\dot\alpha\dot\gamma} \,x_{\beta}^{\dot\gamma}
\right)\partial^{\beta}\, \tilde\Psi= 0\, , \end{eqnarray} \begin{equation}\label{q-costr-y1} \Big(f_{\alpha\beta}+
 m\partial_{\alpha} \partial_{\beta}\Big)\tilde\Psi=0\,,\qquad\qquad
\Big(\bar f_{\dot\alpha\dot\beta}+ m \bar\partial_{\dot\alpha}\bar\partial_{\dot\beta}\Big)\tilde\Psi=0\,. \end{equation}

Let us consider the wave functions with polynomial dependence with respect to $y\equiv y^{\alpha}$ and $\bar y\equiv \bar y^{\dot\alpha}$
\begin{equation}\label{WF-1} \tilde\Psi(x,f, \bar f, y,\bar y)= \sum_{k,n=0}^{\infty}\frac{1}{k!\,n!}\,y^{\alpha_1}...y^{\alpha_k}\, \bar
y^{\dot\beta_1}...\bar y^{\dot\beta_n} \,\tilde\Psi^{(k,n)}_{\alpha_1...\alpha_k\,\dot\beta_1...\dot\beta_n}(x,f,\bar f)\,. \end{equation} Then the
constraints (\ref{q-costr-y1}) for the wave function (\ref{WF}) lead to expressing of all components $\tilde\Psi^{(k,n)}$, $k>1$, $n>1$ by
$\tilde\Psi^{(0,0)}$, $\tilde\Psi^{(1,0)}$, $\tilde\Psi^{(0,1)}$ and $\tilde\Psi^{(1,1)}$. For example, $$ \tilde\Psi^{(2,0)}_{\alpha\beta}= -
m^{-1}f_{\alpha\beta} \tilde\Psi^{(0,0)}\,,\qquad \tilde\Psi^{(0,2)}_{\dot\alpha\dot\beta}= - m^{-1}\bar f_{\dot\alpha\dot\beta} \tilde\Psi^{(0,0)}\,, $$
$$ \tilde\Psi^{(2,1)}_{\alpha\beta\dot\gamma}= - m^{-1}f_{\alpha\beta} \tilde\Phi^{(0,1)}_{\dot\gamma}\,,\qquad
\tilde\Psi^{(1,2)}_{\gamma\dot\alpha\dot\beta}= - m^{-1}\bar f_{\dot\alpha\dot\beta} \tilde\Psi^{(1,0)}_{\gamma}\,, $$ $$ \qquad \qquad
\tilde\Psi^{(3,1)}_{\alpha\beta\gamma\dot\gamma}= - m^{-1}f_{\alpha\beta} \tilde\Psi^{(1,1)}_{\gamma\dot\gamma}\,,\qquad
\tilde\Psi^{(1,3)}_{\gamma\dot\alpha\dot\beta\dot\gamma}= - m^{-1}\bar f_{\dot\alpha\dot\beta} \tilde\Psi^{(1,1)}_{\gamma\dot\gamma}\,,\qquad \mbox{etc}.
$$

Thus, if $m\neq 0$ the fields in the expansion  (\ref{WF-1}) are determined by ten-dimensional ``generalized spin zero'' field
\begin{equation}\label{g-spin0} \tilde\Psi^{(0,0)}(x,f,\bar f)\,, \end{equation} two ``generalized spin half'' fields \begin{equation}\label{g-spin12}
\tilde\Psi^{(1,0)}_{\alpha}(x,f,\bar f)\,,\qquad \tilde\Psi^{(0,1)}_{\dot\beta}(x,f,\bar f) \end{equation} and ``generalized spin one'' field
\begin{equation}\label{g-spin1} \tilde\Psi^{(1,1)}_{\alpha\dot\beta}(x,f,\bar f)\,. \end{equation} The constraints (\ref{q-costr-y1}) provide the following
constraints for the fields (\ref{g-spin0}), (\ref{g-spin12}), (\ref{g-spin1}): \begin{equation}\label{con-spin0}
f^{\alpha\beta}f_{\alpha\beta}\tilde\Psi^{(0,0)}(x,f,\bar f)=0\,,\qquad \bar f^{\dot\alpha\dot\beta}\bar f_{\dot\alpha\dot\beta}\tilde\Psi^{(0,0)}(x,f,\bar
f)=0\,, \end{equation} \begin{equation}\label{con-spin12} f_{\alpha}{}^{\beta}\tilde\Psi^{(1,0)}_{\beta}(x,f,\bar f)=0\,,\qquad \bar
f_{\dot\alpha}{}^{\dot\beta}\tilde\Psi^{(0,1)}_{\dot\beta}(x,f,\bar f)=0\,, \end{equation} \begin{equation}\label{con-spin1}
f_{\alpha}{}^{\beta}\tilde\Psi^{(1,1)}_{\beta\dot\beta}(x,f,\bar f)=0\,,\qquad \bar
f_{\dot\alpha}{}^{\dot\beta}\tilde\Psi^{(1,1)}_{\beta\dot\beta}(x,f,\bar f)=0\,. \end{equation}

{}From the equations (\ref{q-costr-x1}), (\ref{q-costr-x1a}) for the unconstrained component (\ref{g-spin12}), (\ref{g-spin1}) one obtain the relations
\begin{equation}\label{Dir-12} \left(\partial^{\alpha\dot\beta}- i
\,e\,f^{\alpha\gamma}\,x^{\dot\beta}_{\gamma}\right)\tilde\Psi^{(0,1)}_{\dot\beta}(x,f,\bar f)= 0\, ,\qquad \left(\partial^{\beta\dot\alpha}- i \,e\,\bar
f^{\dot\alpha\dot\gamma} \,x^{\beta}_{\dot\gamma} \right)\tilde\Psi^{(1,0)}_{\beta}(x,f,\bar f)= 0\, , \end{equation} \begin{equation}\label{Dir-1}
\left(\partial^{\alpha\dot\beta}- i  \,e\,f^{\alpha\gamma}\,x^{\dot\beta}_{\gamma}\right)\tilde\Psi^{(1,1)}_{\beta\dot\beta}(x,f,\bar f)= 0\, ,\qquad
\left(\partial^{\beta\dot\alpha}- i \,e\,\bar f^{\dot\alpha\dot\gamma} \,x^{\beta}_{\dot\gamma} \right)\tilde\Psi^{(1,1)}_{\beta\dot\beta}(x,f,\bar f)= 0\,
, \end{equation} which have the form of the Dirac equations in a constant electromagnetic field, with electromagnetic potential
$\mathscr{A}_{\mu}=f_{\mu\nu}x^\nu$. Contrary to the standard approach for Dirac spin-half field, the wave functions in (\ref{Dir-12}) depend also on
continuous electromagnetic field strength coordinates $f_{\alpha\beta}$, $\bar f_{\dot\alpha\dot\beta}$. This additional dependence of the wave functions
can not be generated only by minimal coupling of the external electromagnetic field. We do not see yet the relationship of our description of interacting
HS fields to the approaches proposed in recent papers \cite{PRSag,BuchSZ}, however it would be interesting to find such a link.

Generalized spin-zero field $\tilde\Psi^{(0,0)}(x,f,\bar f)$ is described by generalized Klein-Gordon equation, which follows from the constraint
\begin{equation}\label{KG-gen} \hat T^{\alpha\dot\alpha}\hat T_{\alpha\dot\alpha}\,\tilde\Psi\approx 0\,. \end{equation} Taking into account that
\begin{equation}\label{KG-op} \begin{array}{rcl} \hat T^{\alpha\dot\alpha}\hat T_{\alpha\dot\alpha}&=&
-\partial^{\alpha\dot\alpha}\partial_{\alpha\dot\alpha} +2ie\left(f^{\alpha\beta}x^{\dot\alpha}_{\beta} +\bar
f^{\dot\alpha\dot\beta}x^{\alpha}_{\dot\beta}\right)\partial_{\alpha\dot\alpha}\\[6pt] && +{\textstyle\frac12}\,e^2\left(f^{\alpha\beta}f_{\alpha\beta} +
\bar f^{\dot\alpha\dot\beta}\bar f_{\dot\alpha\dot\beta}\right)x^{\gamma\dot\gamma}x_{\gamma\dot\gamma} -2e^2f_{\alpha\beta}\bar
f_{\dot\alpha\dot\beta}x^{\beta\dot\alpha}x^{\alpha\dot\beta}\\[6pt] && -2\left(i\partial^{\alpha\dot\alpha}+ef^{\alpha\beta}x^{\dot\alpha}_{\beta} + e\bar
f^{\dot\alpha\dot\beta}x^{\alpha}_{\dot\beta}\right)\partial_{\alpha}\bar\partial_{\dot\alpha}\,, \end{array} \end{equation} we obtain the generalized
Klein-Gordon equation for spin-zero field \begin{equation}\label{KG-0} \left[ -\Box +2ie\left(f^{\alpha\beta}x^{\dot\alpha}_{\beta} +\bar
f^{\dot\alpha\dot\beta}x^{\alpha}_{\dot\beta}\right)\partial_{\alpha\dot\alpha} +{\textstyle\frac12}\,e^2\Big( f^2+\bar f^2 \Big)x^{2}
-2e^2f_{\alpha\beta}\bar f_{\dot\alpha\dot\beta}x^{\beta\dot\alpha}x^{\alpha\dot\beta}\right]\tilde\Psi^{(0,0)}=0\,, \end{equation} where
$\Box:=\partial^{\alpha\dot\alpha}\partial_{\alpha\dot\alpha}$, $x^2:=x^{\alpha\dot\alpha}x_{\alpha\dot\alpha}$, $f^2:=f^{\alpha\beta}f_{\alpha\beta}$,
$\bar f^2:=\bar f^{\dot\alpha\dot\beta}\bar f_{\dot\alpha\dot\beta}$. It should be emphasized that due to the equations (\ref{Dir-1}) and the constraints
(\ref{con-spin1}) the last term in the operator (\ref{KG-op}) does not contribute to the equation (\ref{KG-0}) and we obtain finally the Klein-Gordon
equation in constant EM field.

The solutions of the equations  (\ref{con-spin0})-(\ref{con-spin1}) can be represented as the Fourier transforms \begin{eqnarray}
\tilde\Psi^{(0,0)}(x,f,\bar f)&=&\int d{}^{\,6}\!z\, e^{-i(fz+\bar f \bar z)} \,\Psi^{(0,0)}(x,z,\bar z) \,,\label{ser0}\\
\tilde\Psi^{(1,0)}_{\gamma}(x,f,\bar f)&=&\int d{}^{\,6}\!z\, e^{-i(fz+\bar f \bar z)} \,\Psi^{(1,0)}_{\gamma}(x,z,\bar z) \,,\label{ser12a}\\
\tilde\Psi^{(0,1)}_{\dot\gamma}(x,f,\bar f)&=&\int d{}^{\,6}\!z\, e^{-i(fz+\bar f \bar z)} \,\Psi^{(0,1)}_{\dot\gamma}(x,z,\bar z)\,,\label{ser12b}\\
\tilde\Psi^{(1,1)}_{\gamma\dot\gamma}(x,f,\bar f)&=&\int d{}^{\,6}\!z\, e^{-i(fz+\bar f \bar z)} \,\Psi^{(1,1)}_{\gamma\dot\gamma}(x,z,\bar z)
\,,\label{ser1} \end{eqnarray} where \begin{eqnarray} \Psi^{(0,0)}(x,z,\bar z)&=&
\sum_{k,n=0}^{\infty}\frac{1}{k!n!}\,z^{\alpha_1\beta_1}...z^{\alpha_k\beta_k}\, \bar z^{\dot\alpha_1\dot\beta_1}...\bar z^{\dot\alpha_n\dot\beta_n}
\,\phi^{(2k,2n)}_{(\alpha_1\beta_1...\alpha_k\beta_k)\,(\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n)}(x)\,,\label{com-ser0}\\
\Psi^{(1,0)}_{\gamma}(x,z,\bar z)&=& \sum_{k,n=0}^{\infty}\frac{1}{k!n!}\,z^{\alpha_1\beta_1}...z^{\alpha_k\beta_k}\, \bar
z^{\dot\alpha_1\dot\beta_1}...\bar z^{\dot\alpha_n\dot\beta_n}
\,\phi^{(2k+1,2n)}_{(\gamma\alpha_1\beta_1...\alpha_k\beta_k)\,(\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n)}(x)\,,\label{com-ser12a}\\
\Psi^{(0,1)}_{\dot\gamma}(x,z,\bar z)&=& \sum_{k,n=0}^{\infty}\frac{1}{k!n!}\,z^{\alpha_1\beta_1}...z^{\alpha_k\beta_k}\, \bar
z^{\dot\alpha_1\dot\beta_1}...\bar z^{\dot\alpha_n\dot\beta_n}
\,\phi^{(2k,2n+1)}_{(\alpha_1\beta_1...\alpha_k\beta_k)\,(\dot\gamma\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n)}(x)\,,\label{com-ser12b}\\
\Psi^{(1,1)}_{\gamma\dot\gamma}(x,z,\bar z)&=& \sum_{k,n=0}^{\infty}\frac{1}{k!n!}\,z^{\alpha_1\beta_1}...z^{\alpha_k\beta_k}\, \bar
z^{\dot\alpha_1\dot\beta_1}...\bar z^{\dot\alpha_n\dot\beta_n}
\,\phi^{(2k+1,2n+1)}_{(\gamma\alpha_1\beta_1...\alpha_k\beta_k)\,(\dot\gamma\dot\alpha_1\dot\beta_1...\dot\alpha_n\dot\beta_n)}(x)\label{com-ser1}
\end{eqnarray} have polynomial dependence on $z$, $\bar z$ and the component fields $\phi^{(k,n)}_{(\alpha...)\,(\dot\alpha...)}$ are symmetric with
respect to all undotted and dotted spinor indices, as the component fields considered in previous subsection. The fields (\ref{ser0})-(\ref{ser1}) have
complicated, nonpolynomial dependence on the variables $f$, $\bar f$. In conclusion, generalized Dirac equations (see (\ref{Dir-12})-(\ref{Dir-1})) and
Klein-Gordon equation (\ref{KG-0}) yield nontrivial, nonminimal coupling of these component fields to the constant EM field.

\subsection{The link between constant torsion in tensorial sector and \\ constant EM field background}

{}From the equations (\ref{Dir-12}), (\ref{Dir-1}) and (\ref{KG-0}) we see that for the link of different spins there is responsible EM coupling described
by nonvanishing parameter $e$. Indeed one can show that if the torsion in six tensorial dimensions of Maxwell space-time depends on the $D=4$ space-time
coordinates it can be reinterpreted as a coupling to an Abelian gauge potential. Let us introduce the following ``block-diagonal'' 10-bein
$E_{AB}{}^{CD}=\left( \delta_\alpha^\gamma \delta_{\dot\beta}^{\dot\delta}, E_{\alpha\dot\beta}{}^{\gamma\delta},
E_{\alpha\dot\beta}{}^{\dot\gamma\dot\delta}\right)$ in the tensorial space $\left( x^{\alpha\dot\beta}, z^{\alpha\beta}, \bar
z^{\dot\alpha\dot\beta}\right)$ \begin{equation}\label{cov-1-N} \nabla_{\alpha\dot\beta}=\partial_{\alpha\dot\beta} +
E_{\alpha\dot\beta}{}^{\gamma\delta}(x)\nabla_{\gamma\delta}+ E_{\alpha\dot\beta}{}^{\dot\gamma\dot\delta}(x)\nabla_{\dot\gamma\dot\delta}\,,
\end{equation} \begin{equation}\label{cov-2-N} \nabla_{\alpha\beta}=\partial_{\alpha\beta}\,,\qquad
\nabla_{\dot\alpha\dot\beta}=\partial_{\dot\alpha\dot\beta}\,. \end{equation} If we consider the plane wave solutions in additional dimensions, one can
replace (see (\ref{op-real1-a})) the derivatives  (\ref{cov-2-N}) by constant tensors $f_{\alpha\beta}$, $\bar f_{\dot\alpha\dot\beta}$ describing
additional tensorial momenta. In such a case the derivative  (\ref{cov-1-N}) can be written as the Abelian gauge-covariant derivative
\begin{equation}\label{cov-3-N} \nabla_{\alpha\dot\beta}=\partial_{\alpha\dot\beta} + \mathscr{A}_{\alpha\dot\beta}(x)\,, \end{equation} where
$\mathscr{A}_{\alpha\dot\beta}(x)=E_{\alpha\dot\beta}{}^{\gamma\delta}(x)f_{\gamma\delta}+ E_{\alpha\dot\beta}{}^{\dot\gamma\dot\delta}(x)\bar
f_{\dot\gamma\dot\delta}$. In Maxwell tensorial space additional tensorial coordinates are twisted by a constant torsion, the functions
$E_{\alpha\dot\beta}{}^{\gamma\delta}(x)$ and $E_{\alpha\dot\beta}{}^{\dot\gamma\dot\delta}(x)$ are linear in $x$, and we obtain in (\ref{cov-3-N}) the
Abelian gauge field four-potential $\mathscr{A}_{\alpha\dot\beta}$ describing constant electromagnetic field strength ($\bar
f_{\dot\alpha\dot\beta}=(f_{\alpha\beta})^\dagger$) \begin{equation}\label{const-A} \mathscr{A}_{\alpha\dot\beta}=
f_{\alpha}^{\,\gamma}x_{\gamma\dot\beta}+\bar f_{\dot\beta}^{\,\dot\gamma}x_{\alpha\dot\gamma}\,. \end{equation} It can be added that the translations
$x_{\alpha\dot\beta}\to x_{\alpha\dot\beta} +a_{\alpha\dot\beta}$ modify (\ref{const-A}) by a constant term, which can be however compensated by the
Abelian gauge transformation of $\mathscr{A}_{\alpha\dot\beta}$, what leads to the translational invariance of covariant derivative
(\ref{cov-3-N}).\footnote{We thank E.\,Ivanov for this observation.}

\setcounter{equation}{0} \section{Final remarks}

In this paper we introduced in ten-dimensional tensorial space the Maxwell-invariant spinorial particle model with auxiliary spinor variables, which after
its first quantization provides the generalization of massless conformal HS fields and define the infinite-dimensional Maxwell-HS field multiplets. These
multiplets of Maxwell HS fields should be further studied, in particular their relation with free massless conformal HS fields and the possibility of their
derivation from an action principle. New multiplets describe particular field-theoretic realizations of Maxwell algebra with vanishing four Casimirs
$C^{Max}_1$, $C^{Max}_2$, $C^{Max}_3$, $C^{Max}_4$ (see (\ref{Cas-fix})). We recall that the mass-shall condition $C^{Max}_1=0$, due to the presence in
$C^{Max}_1$ of the term proportional to relativistic angular momentum ($M_{\alpha\beta}$, $\bar M_{\dot\alpha\dot\beta}$), can be possibly linked with the
description of spin-dependent mass spectrum for Regge trajectories.

The infinite-dimensional sets of Maxwell-HS field which define the realization $T^{(k,n)}$ of Maxwell algebra is para\-met\-rized by two natural numbers
$k=0,1,2,...$, $n=0,1,2,...$. These numbers describe the minimal value of Lorentz spins ($j_1{=}\frac{k}{2},j_2{=}\frac{n}{2}$) in the multiplet of fields
$\phi^{(k+2p,n+2r)}_{\alpha_1...\alpha_{k+2p}\,\dot\beta_1...\dot\beta_{n+2r}}(x) \in T^{(k,n)}$, where $p=0,1,2,...$, $r=0,1,2,...$. It follows that the
representation $T^{(\tilde k,\tilde n)}$ if $\tilde k>k$, $\tilde n>n$ respectively for even and for odd values of ${( k, n)}$, ${(\tilde k,\tilde n)}$, is
included in the bosonic (fermionic) representation $T^{(k,n)}$, i.e.   $T^{(\tilde k,\tilde n)}\subset T^{(k,n)}$. The largest ``master'' bosonic
realization, with component fields having all integer spins $s=\frac12(j_1+j_2)$, is given by $T^{(0,0)}$; two maximal chiral and antichiral fermionic
realizations, with half-integer spins, are provided by $T^{(1,0)}$ and $T^{(0,1)}$.

By considering the particle model on extended space-time ($x_{\alpha\dot\beta}$, $z_{\alpha\beta}$, $\bar z_{\dot\alpha\dot\beta}$, $\lambda_{\alpha}$,
$\bar\lambda_{\dot\alpha}$) and its quantization we have shown how the field-theoretic realizations of Maxwell algebra in such ten-dimensional tensorial
space can be used for the introduction of infinite-dimensional $D=4$ Maxwell-HS field multiplets with coupled spin components. The Maxwell-covariant
description of $D=4$ Maxwell-HS fields requires the presence of space-time-dependent coupling terms between different spin fields which can be also
interpreted (see (\ref{Dir-12}), (\ref{Dir-1})) as following from the electromagnetic covariantization of space-time derivatives in the presence of
constant EM background field strength.

In conclusion we would like to comment that despite the remaining open questions we hope that our model provides a step in understanding of
the theory of interacting HS fields.

\section*{Acknowledgements}

\noindent The authors would like to thank J.\,Buchbinder, E.\,Ivanov, P.\,Kosinski  and D.\,Sorokin for valuable remarks. We acknowledge a support from the
grant of the Bogoliubov-Infeld Programme, the grant of the INFN-BLTP JINR collaboration and RFBR grants 09-01-93107, 11-02-90445, 12-02-00517 (S.F.), as
well as from the Polish Ministry of Science and Higher Educations grant No.~N202331139 and Polish National Center of Science (NCN) research project
No.~2011/01/ST2/03354 (J.L.). S.F. thanks the members of the Institute of Theoretical Physics at Wroclaw University and Dipartimento di Fisica ``Galileo
Galilei'' at Universit\'{a} degli Studi di Padova for the warm hospitality at different stages of this study. J.L. thanks CERN Theory Division for the
hospitality at the final stage of this work.

\renewcommand\theequation{A.\arabic{equation}} \setcounter{equation}0 \section*{Appendix:   Different dimensionalities of tensorial coordinates and some
consequences}

We can arbitrarily change the mass dimensionality of the generators ; consequently the relation (\ref{M-alg}) is replaced by relation (\ref{M-alg-m}).
One gets in rescaled case
\begin{equation}\label{dim-ch}
[Z_{\alpha\beta}]=[\bar Z_{\dot\alpha\dot\beta}]=2-\xi\,,
\end{equation}
what implies
\begin{equation}\label{dim-z}
[z^{\alpha\beta}]=[\bar z^{\dot\alpha\dot\beta}]=
[\omega_{(Z)}^{\alpha\beta}]=[\bar\omega_{(Z)}^{\dot\alpha\dot\beta}]=-2+\xi\,.
\end{equation}

The parameters introduced in (\ref{M-alg-m}) will modify the formulae (\ref{M-om}) as follows \begin{equation}\label{M-om-m} \omega^{\alpha\beta}=   d
z^{\alpha\beta} + eM^{\,\xi}x^{(\alpha\dot\gamma}d x^{\beta)}_{\dot\gamma}\,,\qquad \bar\omega^{\dot\alpha\dot\beta}= d\bar z^{\dot\alpha\dot\beta}+
eM^{\,\xi}x^{\gamma(\dot\alpha}d x^{\dot\beta)}_{\gamma}\,. \end{equation} After inserting relations (\ref{M-om-m}) in (\ref{Maxwell-Lagr}) it follows from
(\ref{dim-z}) that dimensionless action requires the replacement of $m$ by $m^{1-\xi}$. Subsequently we obtain the following modified constraints
(\ref{costr-x})-(\ref{costr-by}) \begin{eqnarray}\label{costr-x-m} T_{\alpha\dot\beta}&=&p_{\alpha\dot\beta}-\lambda_{\alpha}\bar\lambda_{\dot\beta}+
\tilde em\Big(\lambda_{\alpha}\lambda_{\gamma}x^\gamma_{\dot\beta}+\bar\lambda_{\dot\beta}\bar\lambda_{\dot\gamma}x^{\dot\gamma}_{\alpha}\Big)\approx 0\,
,\\[5pt] T_{\alpha\beta}&=&f_{\alpha\beta}-m^{1-\xi}\lambda_{\alpha}\lambda_{\beta}\approx 0\,,\label{costr-y-m}\\[5pt] \bar T_{\dot\alpha\dot\beta}&=&\bar
f_{\dot\alpha\dot\beta}-m^{1-\xi}\bar\lambda_{\dot\alpha}\bar\lambda_{\dot\beta}\approx 0\,,\label{costr-by-m} \end{eqnarray} where the  rescaled
dimensionless coupling constant $\tilde e$ is given by the formula \begin{equation}\label{til-e} \tilde e= \left(\frac{M}{m}\right)^{\xi}e\,.
\end{equation} One can check that the constraints (\ref{costr-x-m}) lead to the basic field equations (\ref{Eq-Dir-comp1-a})-(\ref{Eq-Dir-comp2-a}) and
(\ref{Eq-KG-comp-a}) with the replacement $m\to \tilde e m$. One can also reduce the number of parameters by putting in (\ref{Maxwell-Lagr}) $m=M$. In such
a case $\tilde e=e$ and the theory contains only one geometric mass parameter, determined by the structure constant of the of Maxwell algebra.

We shall make the following comments: \begin{description} \item[i)] If $\xi=0$ and $e\neq 0$ the Maxwell algebra takes its original form \cite{Bac,Schr,B}
and describes the space-time geometry with constant electromagnetic background. We obtain the relations from Sect.\,1--3 with terms in the equations which
couple different spins by terms proportional to $em$. \item[ii)] If $\xi=1$ we have the relation $\tilde e m=eM$. The equations (\ref{costr-y-m}),
(\ref{costr-by-m}) are the same as in the particle model in \cite{BL,BLS,Vas,PST,BBAST,Vas1} providing massless HS free fields, however the eq.
(\ref{costr-x-m}) is modified due to the presence of generalized Maxwell space-time $(x_\mu,z_{\mu\nu})$ with torsion proportional to $eM$. The basic field
equations are obtained from (\ref{Eq-Dir-comp1-a}), (\ref{Eq-Dir-comp2-a}) and (\ref{Eq-KG-comp-a}) by the replacement $m\to M$, i.e. for $\xi=1$ the
dynamical mass parameter in our model disappears from the constraints (\ref{costr-x-m})-(\ref{costr-by-m}) and is transmuted into the geometric one.
\item[iii)] If $\xi=2$ in the Lagrangian  (\ref{Maxwell-Lagr}) the parameter $m$ is replaced by $m^{-1}$. Such choice of Maxwell algebra generators (for
$e=1$) was considered recently in \cite{AKLuk,Sor2,Durka} as the algebraic basis for the generalization of Einstein gravity but the corresponding particle
action  (\ref{Maxwell-act}) is singular in the limit $m\to 0$. \end{description}

redpajama_set_name: RedPajamaArXiv


text:
Q: How do I persist a file on a rpm update? I am writing a rpm spec file and I want to persist a db file during an update.
I was reading the documentation and so far I found the %config modifier that persist configuration files.It is to say something like:
%file
%config(noreplace) foo.db

Is this the right way to persist a file during a rpm update?
Thanks in advance!

A: Directive %ghost.
Files marked as ghost are not shipped in RPM. They are not being installed, but they are owned by package.
You still need to create them in %install. But touching is fine. So:
%install
touch %buildroot/var/foo

%files
%ghost /var/foo

This is intended for db files, log files etc.

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text:
Kálmán Tisza de Borosjenő (archaic English: Coloman Tisza, or Koloman Tisza; 16 December 1830 – 23 March 1902) was the Hungarian prime minister between 1875 and 1890. He is credited with the formation of a consolidated Magyar government, the foundation of the new Liberal Party (1875) and major economic reforms that would both save and eventually lead to a government with popular support. He is the second longest-serving head of government in Hungarian history.

Political career

At the age of 18, Kálmán Tisza witnessed one of the greatest transformations of the political arena in Hungarian history. Hungary's political system changed from being a feudalistic state into a newly established constitutional monarchy that shared many components with modern-day governments. Legislation such as Public Law III abolished the Royal Chancellery and the Residential Council replacing them with a bicameral parliament (House of Lords and House of Representatives). Democratic principles were established with Public Law V that allowed 6.5% of the population to vote (Janos 85). Also, the union of traditional Magyar lands under Public Law VI and VII created a unified Hungary. These powerful reforms led to a nationalist revolt that culminated in the dethroning of the Habsburg dynasty during the Hungarian Revolution of 1848-49.

With the defeat of the Hungarians during the revolution, many of the reforms were revoked and Hungary was put under military dictatorship under Austrian general Julius Haynau. Though the revolution's suppression ended the parliamentary-style government in Hungary, it did not destroy the seeds that were sown by the initial reforms. During 1859 and 1860—after seeing the Hungarian popular support for the Italians during the Austro-Italian wars—Austria began to try new constitutional experiments in Hungary. During this period, Kálmán Tisza was first elected to the newly formed government. Then, in 1867, on behalf of the Hungarian Parliament, Tisza participated in negotiations with Emperor Franz Joseph I that led to the Compromise of 1867 (; ). The importance of this document is that it restored the "Constitutional integrity of Hungary" (Janos 90), with the exception over powers of defense and foreign affairs. These minor concessions by the Emperor soon collated and restored the powers, concerning internal affairs back to the Hungarians. These changed circumstances laid the path for Tisza to rise to the position of Prime Minister. In 1875, he founded the Liberal Party and was elected to the position of Prime Minister of Hungary. The efficiency of the government was initially quite weak and his actions during his 15-year service mainly consisted of reforming the government and the economy.

The newly born government bureaucracy of Hungary was inefficient and lacked a centralized government. One of the first acts performed under the premiership of Kálmán Tisza was the consolidation of power and transformation of the bureaucracy into a single, capable apparatus: "The bureaucracy was in charge of the elections and perpetuating the liberal majority, while parliament and the party would lend an aura of legitimacy to bureaucratic policies and provide a forum to articulate bureaucratic interests" (Janos 97). Kálmán Tisza achieved consolidation of power within the government while Parliament simply served to legitimize those actions. Consolidation of power also consisted of the reform of an incumbent parliament where members came to hold their seats regularly without challenge.

Reform of the House of Magnates in Hungary
469 members were removed under the provisions of the Parliament Act. The number of Members set to 369 members: 205 hereditary peers, 83 church dignitaries, and a new feature, 81 life members. Aristocratic titles were still given by the imperial power but hereditary and life peerages were to be awarded upon the advice of the Prime Minister who, in case of emergency, could seek the appointment of new members to secure the passage of a particular piece of legislation (Janos 99). These reforms allowed the position of the Prime Minister to be the single most important actor in the Hungarian political arena. These reforms by Tisza allowed him to consolidate power within the Hungarian government and also remove much of the influence extended by the Austrians. He helped to finally set in stone the shift of Hungarian political dependence away from the Austrians.

Economic reform
Between 1869 and 1875 (with the establishment of the new Hungarian political system), the Hungarians chose to style their economic system under a French model. The problem they encountered was that their current political system was more advanced in comparison to their archaic economic system. For example, taxation of the people came in the form of quasi-military campaigns that only raised taxes by 11% (Janos 106), while it embittered the rural population. Thus, these 6 years were known as a period of poor management of the economy by a failing government. When Tisza came to power in 1875, he consolidated the economy in many ways similar to his power consolidation of the government. He initiated tax reforms saving the state from bankruptcy. In 1889, Sándor Wekerle became Minister of Finance. He collaborated with Tisza to develop a new tax system which focused on taxing the land. The success of these reforms were tremendous, even though the land tax increased by 30%, the revenues of the government increased by 330% (Janos 108). Between 1880 and 1895, public revenue doubled due to the successful tax reforms. Though the Tisza-Wekerle system saved the government from bankruptcy, the tax system proved to be too harsh and eventually prevented the rise of a domestic market for the products produced by Hungary.

Legacy
The contributions made by Kálmán Tisza during his 15-year premiership were quite tremendous. Although he was born during the midst of a failing Austrian Imperial government in Hungary and he had inherited a failing Hungarian Constitutional government, he managed to turn Hungary into a modern state. He saved his country from going completely bankrupt and consolidated and created an efficient centralized government. His legacy of reform and success gave confidence to a people that were once suppressed by the Austrians and were struggling to master constitutional government. However, he has also been associated with the policy of Magyarization and the imposition of Magyar hegemony over the various linguistic and ethnic groups in Hungary, as well as consolidating the influence of the Magyar country gentry on political life. His son István Tisza also became a notable Hungarian politician.

Orders and decorations
   Austria-Hungary: Grand Cross of the Royal Hungarian Order of Saint Stephen, 1880

Ancestors

References

Bibliography
Andrew C. Janos, The Politics of Backwardness in Hungary 1825–1945, Princeton: Princeton University Press, 1982.

External links

1830 births
1902 deaths
People from Oradea
Hungarian Calvinist and Reformed Christians
Kalman Tisza
Hungarian nobility
Resolution Party politicians
Left Centre politicians
Liberal Party (Hungary) politicians
Prime Ministers of Hungary
Hungarian Interior Ministers
Foreign ministers of Hungary
Finance ministers of Hungary
Grand Crosses of the Order of Saint Stephen of Hungary

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Thinking of my grandfather while watching Lies My Father Told Me DVD
Lies My Father Told Me -The Sequel?
Actress Marilyn Lightstone thrilled with Lies DVD
In Lies My Father Told Me, noted Montreal-born actress Marilyn Lightstone plays one of the starring roles of Anna Herman.
Co-producer Harry Gulkin says Lightstone was right for the role of the mother. Her strength as an actress had been tested in many demanding stage and film roles. In Lies My Father Told Me, her mobile features express and reflect all the trials and tenderness felt by a young woman who is at once wife, daughter, and mother.
Lightstone, a multi‐talented artist, won accolades for her work as Annie . She was also seen in such films as "In Praise of Older Women" (1978), and "The Tin Flute/Bonheur D'Occasion" (1983). She distinguished herself in theatre, starring as Leah in the Los Angelesproduction of "The Dybbuk" playing in New York opposite Lee J. Cobb in "King Lear" and as Masha in Chekhov's "The Seagull" at the Stratford Festival. On television, she co‐starred as Miss Stacy in both the Anne of Green Gables and Road to Avonlea series and made guest appearances on Cheers, Cagney and Lacey, Street Legal and E.N.G. She has written scripts for television and her first novel, Rogues and Vagabonds, received much acclaim. She was the founding "Voice of Bravo", Canada's NewStyleArts Channel where she currently hosts a series called Playwrights and Screenwriters.
Lightstone grew up in Montreal, initially in the Plateau on Clark Street and then in Snowdon. She got an Arts degree from McGill and was a member of the second graduating class of the National Theatre School, moving to Toronto in 1964
What effect did being part of the cast of Lies My Father Told Me have on her career? "Lies My Father Told Me was my first film role after eight years of stage work and it established me as a film actress," she said. "That is not just because I was on the screen, but because it was such a fine and special film and one which would continue to be meaningful, not just for the Jewish community, but in the history of Canadian film. In other words, it had legs."
Lightstone (pictured below in a scene from the movie) is thrilled about the DVD release. "People have been wanting their own copy for years and now it is finally possible," she remarked.
It has been a few years now since Lightstone, now 69, had her last TV role. "There are very few roles for women my age, and when there is one they're usually looking for a tsekrocheneh oldster , preferably one with a Yiddish accent who can play stereotypical bubbies. To cast that, they can do far better than me because I don't fit the bill, and it's not that interesting to me.
Lightstone says she spends half of her time researching, writing and recording her radio show, which is on for two hours every night and which can be heard at www.classical963fm.com between 11p.m. and 1 a.m. Toronto time anywhere in the world. The other half is spent in her studio where she work on the visual arts - painting and photography, and sometimes the two together. "When I was a child I thought I was going to be a painter," she says. Samples of her work can be seen at www.marilynlightstone.com.
"Rest assured, that should something really interesting come along I would be most interested in acting again, but I'm not sitting at home waiting for the phone to ring," she says.
Please read the article below about Lies My Father Told Me and the memories it evoked about my own grandfather.
Posted at 09:47 AM in Film and Leisure, Personal Memories | Permalink | Comments (1)
Hi! This post couldn't be written any better! Reading this post reminds me of my old room mate! He always kept chatting about this. I will forward this page to him. Fairly certain he will have a good read. Thank you for sharing!
Posted by: ผลบอล | November 09, 2013 at 12:34 PM

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How could [God] have shown his mercy more clearly than by taking on himself our condition? For our sake the Word of God became as grass. What better proof could he have given of his love? Scripture says: Lord, what is man that you are mindful of him; why does your heart go out to him? The incarnation teaches us how much God cares for us and what he thinks and feels about us. We should stop thinking of our own sufferings and remember what he has suffered. Let us think of all the Lord has done for us, and then we shall realize how his goodness appears through his humanity. The lesser he became through his human nature the greater was his goodness; the more he lowered himself for me, the dearer he is to me. The goodness and humanity of God our Savior have appeared, says the Apostle.


NEW YORK, AUGUST 9, 2016 – Freelance Sound Mixer Matt Sonnenfeld has been using Sound Devices equipment, such as the 633 and 688 field production mixers, for more than three years. Along with his brother Adam, Sonnenfeld co-owns Four B Productions, Inc., a full-service production company based in Brooklyn, NY. Sonnenfeld has worked on notable television shows, including Made From America on The Travel Channel and Catching Odell, an NFL special.
Currently, Sonnenfeld is working on an upcoming documentary about veterans and post-traumatic stress disorder (PTSD), a personal subject for him as he lost his cousin to PTSD in 2013. The documentary will explore what PTSD is, what treatments are available and evolving, and how the conversation about PTSD is changing. The project is being shot in multiple locations, ranging from hospitals and government buildings, to small law offices. It often involves Sonnenfeld, as a one person crew, conducting interviews within small spaces.
The way that Sonnenfeld has captured content for the documentary has evolved since the project began. Whether shooting with a RED camera or a SONY a7S, Sonnenfeld's PIX-E7 has now become the project workhorse. It serves as recorder as well as his confidence and focus monitor. The PIX-LR, with its high-performance mic preamps, brings professional audio to the monitor via two full sized, low noise, wide gain XLR inputs.
The PIX-LR is an optional PIX-E Series accessory that provides the camera-mount monitors with full-size XLR audio inputs and outputs. It also features signature Sound Devices-designed mic preamps, unclippable limiters, 48 volt phantom power, and high-pass filters, as well as accurate LED metering and dedicated tactile controls. The PIX-LR easily and securely mounts to the bottom of any PIX-E Series monitor via an industry-standard ¼-inch-20 thread screw. Constructed from die-cast aluminum, the PIX-LR derives power from the monitor to which it is attached.
Another PIX-E accessory that is proving its worth on Sonnenfeld's shoots is the SpeedDrive recording and file-delivery enclosure. The SpeedDrive looks like a thumb drive but houses a non-proprietary mSATA SSD—readily available at various retailers and online stores in sizes up to 1TB. While plugged into the back of any PIX-E monitor, the SpeedDrive uses a SATA interface, which is perfect for high-capacity 4K recording. Remove it from the monitor, and the SpeedDrive streamlines the file-delivery process by eliminating the need for special card readers, cables, or docking stations. Just plug it into any USB 3.0 port on a Mac or PC to quickly transfer data.


Please contact us for a detailed catering menu at info@bonjourtexas.com or view the PDf's attached. Merci! Thank you!
An assortment of freshly baked croissants, muffins & danishes.
Served with grapes, berries & clotted cream.
Greek yogurt & honey mixed with granola and fresh berries.
An assortment of pineapple, strawberries & grapes.
Bagel, Cream Cheese, Fruit cup & yogurt parfait.
Choice of muffin, scone or danish with fruit cup & yogurt parfait.
+Turkey, Cheddar, Lettuce all wrapped in flour or whole wheat tortilla- served with mayo.
+Ham, Cheddar, Lettuce all wrapped in flour or whole wheat tortilla- served with mayo.
All sandwiches & wraps wrapped individually & served cold.
* Reece's Peanut Butter (3 tiered, individual cake)*With sandwich or salad order. Dessert Platters are available.
Thinly sliced Prosciutto, turkey, ham & chicken, Swiss Cheese, gruyere, Sharp Cheddar & Kalamata olives. Butter lettuce, tomatoes & cornichons (French pickles) accompany the platter.
Brie, Gouda, Sharp Cheddar, Goat Cheese, Crackers, cornichons (French pickles), olives & fig balsamic dressing all served with fresh baguette.
Sharp Cheddar, Brie, Goat Cheese, Salami Mozzarella rolls, grapes & strawberries served with fruit dip & fig balsamic dressing.
Chocolate chip brownie, Blondie & Mixed nuts brownie.
Assortment of cookies including black & white cookie, jam cookie & more.
Assortment of desserts including eclairs, brownies & cookies.
Freshly brewed 7 Monks coffee (house roast or dark roast) packed in a disposable thermal urn. Beverage service includes sugar, sweeteners, half & half, disposable cups, and beverage napkins.
Freshly brewed hot tea packed in a disposable thermal urn. Beverage service includes sugar, sweeteners, half & half, disposable cups, and beverage napkins.
Freshly brewed iced tea (un sweet & sweet) packed in a disposable thermal urn. Beverage service includes sugar, sweeteners, half & half, disposable cups, and beverage napkins.


Prizes available only for mobile numbers from the Philippines.
1. Form a group of 3-5 people.
2. Make a FUNsign written for, "Jessica's Stories" or "Team JS"
ONLY ONE ENTRY PER GROUP.
The FUNsign with the most likes by the end of the voting period wins! The pictures will be posted after the end of submissions on the Jessica's Stories fanpage.
Each member of the group will win P50.
Examples of FUNsigns can be found here.


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Michigan Seeks Changes to Abuse Reporting Law After Nassar
Like all other states, Michigan requires health providers, psychologists, teachers, police, clergy and others to report suspected child abuse or neglect to authorities
By David Eggert	• Published March 10, 2018 • Updated on November 9, 2018 at 12:45 pm
Michigan is looking to shore up its law that requires certain people to report suspected child sexual abuse to authorities to address gaps that were exposed after disgraced former sports doctor Larry Nassar admitted to sexually assaulting female athletes.
Nassar's victims are spearheading the initiative, saying he could have been stopped decades ago if coaches, athletic trainers or others at Michigan State University had listened to them. More than 250 women and girls have said the now-imprisoned Nassar molested them with his ungloved hands under the guise of medical treatment.
No one has faced charges yet for not reporting the abuse, but multiple investigations are underway into Michigan State's handling of complaints.
Like all other states, Michigan requires health providers, psychologists, teachers, police, clergy and others to report suspected child abuse or neglect to authorities. A bill up for approval by the state Senate would add college employees and youth sports coaches, trainers and volunteers.
Additional legislation would increase potential punishments. Paid professionals who willfully do not report suspected abuse or neglect could face a felony charge and up to two years in prison, up from what is now a misdemeanor punishable by a maximum 93 days in jail.
"It puts stronger incentives in place to properly motivate adults to respond to disclosures of sexual assaults," said Rachael Denhollander, who was 15 when Nassar assaulted her in his campus office in 2000. "As much as it is difficult and as much as we don't want to recognize this fact, there are adults who will not be motivated by an ethical, moral code to report sexual assault of children."
Eleven other states already require college employees to report abuse. Eighteen more require anyone aware of suspected abuse or neglect to report it, according to the Child Welfare Information Gateway, a service of the U.S. Department of Health and Human Services. In five states, all youth coaches — not just those who are school employees — are mandatory reporters.
Michigan isn't the only state to explore changes. Illinois is looking to increase the punishment for not reporting abuse and may require coaches and other athletic workers to undergo training. Legislation in Georgia would give victims of childhood sexual abuse more time to sue for damages — something Michigan is also considering .
Michigan's legislation would address ambiguity surrounding who must report abuse. Nassar's accusers contend in a lawsuit that four current or former Michigan employees they told — including ex- gymnastics head coach Kathie Klages, Nassar's physician supervisors and a psychology professor who saw one victim through his separate private practice — were mandated reporters already.
The bill would cover college workers along with coaches, assistant coaches and trainers involved in youth sports that are both affiliated and unaffiliated with schools and universities, such as Twistars, a Lansing-area gymnastics club where Nassar molested athletes.
"Enablers need to be held accountable," said Larissa Boyce, who said she was 16 when she complained about Nassar to Klages in 1997, while she was training with the Spartan youth gymnastics team.
Boyce said Klages dissuaded her from taking it further despite confirming that a 14-year-old girl had received similar "treatments." Klages has denied that anyone reported Nassar to her.
While the legislation has bipartisan support, it has some opponents.
The American Civil Liberties Union of Michigan says volunteer coaches, who can include high school students and young adults, do not get training they would need to recognize signs of abuse or neglect. Kimberly Buddin, the group's policy council, also said harsher criminal penalties could lead to unintended consequences in instances where no abuse has occurred.
"We don't want to create a culture where people are just reporting things that don't need to be reported because they're afraid of going to jail," Buddin said.
But Republican Sen. Margaret O'Brien, the main bill sponsor, said not much is asked of mandatory reporters.
"This is not a difficult thing to do. All you have to state is the people involved and what information you were given," she said. "You don't have to investigate. Mandated reporters are not judge and jury."
GeorgiaMichiganhead coachassistantIllinois


Get your strawberries and cream ready; Wimbledon 2016 isn't too far away. Reigning champions, the seemingly unstoppable Serena Williams and Novak Djokovic, will be hoping to retain their titles, while home fans will be backing Andy Murray and Laura Robson. What's certain is that millions across the world will be tuning in to enjoy this festival of tennis.
Part of what makes Wimbledon so special is tradition; all-white shirts and shorts, celeb-spotting in the Royal Box and the gathering of spectators not fortunate enough to win Centre Court tickets on "Henman Hill" (or "Murray Mound"). However, Wimbledon has also embraced technological innovation, with Hawk-Eye and retractable roofs being installed in recent years. Over the next decade, we're expecting the IoT to improve the tournament in all sorts of ways. So, what might Wimbledon 2025 look like?
The quality of tennis is already extremely high, with players like Djokovic, Federer, Williams and Radwanska on show, but in 2025 we think it will reach new heights thanks to the IoT. One reason is the connected racket, which has already been developed by Babolat and is beginning to see mainstream adoption.
Imagine a world where tennis players could immediately identify the weaker areas of their game. It's a dream fulfilled by the connected racket. These rackets are fitted with embedded sensors, capable of collecting precise data on the player's performance. By downloading a smartphone app, the player can then analyse the data as soon as possible. Already, the technology is having an impact – the International Tennis Federation has approved the technology and, during last year's Roland Garros, data from connected rackets was made available to fans on the Internet, enabling them to better understand how their idols play the game.
At Wimbledon 2025, not only might players be equipped with connected rackets – they could also be using wearables, equipped with interactive displays and voice recognition. These will combine with the connected racket to provide insight into player performance, accessible in real-time. What this could mean is the regular player breaks could evolve from just a breather into crucial periods for analyzing performance and adjusting tactics.
The IoT is also great news for tennis event organizers – and by 2025 could be generating extra revenue for Wimbledon. As Lewis Sherr, Chief Revenue Officer at the US Tennis Association, highlighted in an interview with CIO, the IoT brings new opportunities for sharing big data with sponsors and demonstrating their visibility and impact in real-time. To understand more about IoT monetization, see our page here.
Anyone who's been to Wimbledon will tell you it's a fantastic experience, but will probably warn you that there's a lot of queuing. Fortunately, by 2025, you could be able to gain entry to the grounds with your smartphone. By downloading a special Wimbledon app, where your ticket details would be stored, you'd be able to gain entry by tapping your digital ticket against the NFC card reader. Getting into Wimbledon might be as quick as an Andy Roddick serve!
Being a tennis fan in 2025 could be a more interactive experience. By downloading a specialist smartphone app, you'd be able to receive all the Wimbledon news during the tournament. During the match, you'd view players' performance data in real-time. Plus, viewers at home would be able to enjoy the spectacle from a court-side seat, thanks to Virtual Reality (VR). By just putting their smart goggles on, they might be transported to Centre Court to enjoy the action.
As you can see, Wimbledon 2025 is set to be a connected tournament. The IoT could change the competition in all sorts of ways, enhancing the experience for players and fans. So to anyone saying 'you cannot be serious!' about the potential of IoT – we certainly are!
What are your expectations for sport in 2025? Let us know by tweeting to @Gemalto, or by posting a comment below.


clerkships, for board prep, or as a handy clinical reference. Richard A.
answers to help you better meet the challenges you face every day.
Stay current with the proven question and answer format of the highly acclaimed Secrets Series.
Identify key facts and secrets using the Top 100 Secrets section.
Stay current on the latest standards in pediatric care thanks to extensive updates throughout the text.