text:
\section{ Introduction}
In this paper first we  review the derivation
of the $ q \bar q $ and
the $ 3q $ semirelativistic potentials for dynamical quarks as has been
given in preceding papers$^{1}$ (for a general review
 on the subject see$^2$) and introduce
 some significant improvements.  Then we show that, under the same
 assumptions and in the case of spinless quarks, a Bethe--Salpeter
 equation with a confining kernel can be obtained.\par
The basic objects considered in the derivation are the appropriate Wilson loop
integrals $ W_{q \bar q} $ and $ W_{3q} $ and the basic assumptions are:
\par
i)  the quantities
 $ i \ln W $ can be expressed as the sum of a short range
contribution $ i \ln W^{SR} $ and a long range one $ i \ln W^{LR} $ ;
\par
ii) the SR--term can be obtained simply from a perturbative expansion
and the LR--term from a strong coupling expansion
(in practice by the area law).
\par
The improvement consists in the fact that
an  ad--hoc explicit instantaneous approximation is no longer required
and only expansions in the quark velocities are used.
Furthermore, the $O (\alpha^{2}_{\rm s}) $
 contribution is explicitly taken into
account in the static part of the potential and it is shown that
a covariant Lorentz gauge as well as the
Coulomb gauge can be used.

As it is  well known,
the arguments in favour of the two assumptions are
 asymptotic freedom and
the observation that the SR--part of the potential vanishes for $ r \rightarrow
\infty $, while the LR--part vanishes for $ r \rightarrow 0 $. Obviously, with
the simple additivity assumption i),
the resulting potential or kernel
 is expected to be inaccurate at intermediate distances;
interferences of the two mechanisms should be important there.
However, no attempt is made in this paper to use a more
 sophisticated approximation
scheme of the type proposed e.g. in Refs.$^{3}$
 ( see also$^4$).

In Sec. 2 we discuss the evaluation of the Wilson loop integrals, in Secs. 3
and  4 we derive the $  q \bar q $  and the $ 3q $
potentials respectively, in Secs. 5 and 6 we sketch the derivation
 of the flux--tube lagrangian and of the Bethe--Salpeter equation.

\section{ Wilson loop integrals}
For the $q\overline{q}$ case the basic object is
 \begin{equation}
W_{q\overline{q}} = \frac{1}{3} \left\langle {\rm Tr \   P}
 \exp \left( ig \oint_{\Gamma} dx^{\mu} \
 A_{\mu}(x) \right) \right\rangle \> .
\end{equation}
Here the integration loop $\Gamma$ is assumed to be made by an
arbitrary  world line
$\Gamma_1$ between an
initial position ${\bf y}_1$ at the time $ t_{\rm i} $ and a final one ${\bf
x}_1$ at the time
  $ t_{\rm f} $  for the quark ($t_{\rm i} < t_{\rm f}$), a similar world
line $\Gamma_2$ described
 in the reverse direction from ${\bf x}_2$ at the time $t_{\rm f}$
to ${\bf y}_2$ at the time $t_{\rm i}$ for the antiquark and two straight lines
at fixed times which  connect ${\bf x}_1$ to ${\bf x}_2$, ${\bf y}_2$
to ${\bf y}_1$ and close
the contour. As usual $ A_{\mu} (x) =
\frac{1}{2} {\lambda}_ {a} A_{\mu} ^{a} (x) $,
  P prescribes the ordering
of the color matrices (from right to left) according to the direction fixed
on the loop and the angular brackets denote
 the functional integration.\par
Integrating explicitly the fermion fields, for any functional
 of the gauge field
alone one obtains
\begin{equation}
\langle f[A] \rangle = \frac{\int {\cal D}[A] M_f(A)
f[A] e^{iS[A]}}
{\int {\cal D}[A] M_f(A) e^{iS[A]}} \> ,
\label{eq:due}
\end{equation}
where $ S[A] $ denotes the pure gauge action
plus the gauge--fixing terms and $ M_{\rm f} [A] $ is the fermionic
determinant
\begin{eqnarray}
  M_{\rm f} [A]  & =&   {\rm Det} \prod_{j} [ 1 +
                             i g A (i \partial - m_j )^{-1} ] =
  \sum_{j} [g \int {\rm d}^4 x
 {\rm Tr} (i A(x) S_{\rm F}^{(m_j)}(0) )\nonumber \\
& - &{1 \over 2} g^2
 \int {\rm d}^4 x \int {\rm d}^4 y {\rm Tr}
 ( A(x) i S_{\rm F}^{(m_j)}(x-y) A(y) i S_{\rm F}^{(m_j)}(y-x) )
+ ... ].
\label{eq:tre}
\end{eqnarray}
\indent
Using the above equations and writing the gauge field lagrangian as
the sum of the free and the interaction parts, $ {\cal L}(A)
={\cal L}_0 + {\cal L}_{\rm int} $,
we have the perturbative expansion
\begin{eqnarray}
& & W_{q \bar{q}}^{\rm pert}  = {1 \over 3} \sum_{n=0}^{\infty}
  \sum_{p=0}^{\infty} {1 \over n!p!} \langle  {\rm  Tr} {\rm P}
 (ig \oint
 {\rm d}z^{\mu}
             A_{\mu} )^n (i \int {\rm d}^4 x {\cal L}_{\rm int}(x))^p
 \rangle_0 =
\nonumber \\
& &  ={1 \over 3} \sum_{n=0}^{\infty} \sum_{p=0}^{\infty} {(ig)^n i^p \over p!}
\int {\rm d}^4 x_1 ... \int {\rm d}^4
x_p
 \oint ... \oint_{z_{1} > z_{2} > \dots > z_n} {\rm d}z_{1}^{\mu
_1} ... {\rm d}z_{n}^{\mu_n}\nonumber \\
& & \langle {\rm Tr} [A_{\mu_1}(z_1) \dots
 A_{\mu_n}(z_n)]
 {\cal  L}_{\rm int}(x_1)\dots {\cal L}_{\rm int}(x_p) \rangle_0,
\label{eq:quattro}
\end{eqnarray}
where, due to (\ref{eq:tre}), the single terms must be understood
  as expansions in $g$ in turn.
Then, identifying $ W^{\rm SR} $ with $ W^{\rm pert} $
according to  assumption ii),  we obtain in graphical
 terms
(we omit graphs that are obtained by permutation of  other ones or
 completely cancelled by renormalization)
\vfill\eject
\begin{figure}
\vspace{4 truecm}
\end{figure}
\begin{equation}
                  i \ln W_{q \bar q}^{\rm SR} =
\label{eq:cinque}
\end{equation}
\noindent
 where
  the external circuit stands for the Wilson loop $\Gamma$,
 and the inserted lines for
ordinary free propagators. Notice the term which includes
 a quark-antiquark loop,
which obviously  comes from (\ref{eq:tre}).

The various quantities occurring in (\ref{eq:cinque})
have been extensively studied from the point of view of
re\-nor\-ma\-li\-za\-tion$^{5}$.
 To our knowledge however
no explicit evaluation in closed
form has been given other than in very special cases$^6$.
For the purpose of the derivation of a semirelativistic
potential, an evaluation in terms of
  an expansion in the quark velocities
 shall be sufficient.

Let  $ (z_j^0 = t_j, \   {\bf z}_j = {\bf z}_j(t)) $ be the equation
 for the world
lines  of the quark and the antiquark
 and set $ \dot{z}^{\mu}_j = dz^{\mu}_j /dt = (1,\   \dot{\bf z}_j)
$. The first--order term in
  $\alpha_{\rm s} = g^2/4 \pi $  can be written explicitly as
\begin{equation}
(i \ln W^{\rm SR})^{(1)}_{q \bar{q}}
 ={4 \over 3} g^2 \int_{t_{\rm i}}^{t_{\rm f}}
{\rm d}t_1 \int_{t_{\rm i}}^{t_{\rm f}} {\rm d}t_2 \dot{z}_1^{\mu}(t_1)
 \dot{z}_2^{\nu}(t_2)
D_{\mu \nu}(z_1(t_1) - z_2(t_2))\> ,
\label{eq:sex}
\end{equation}
where the limit for large $ t_{\rm f} - t_{\rm i} $ has been understood and
the contribution from the equal--time lines are
neglected. Performing the change of
variables $ t = {t_1 + t_2 \over 2}$, $ \tau = t_1 - t_2 $,
expanding $ {\bf z}_1 $ and $ {\bf z}_2 $ around $ t $,
\begin{equation}
  {\bf z}_{1}(t_{1}) ={\bf z}_{1}(t) + {1 \over 2} \tau \dot{\bf z}_{1}(t)
    +{1 \over 8} \tau^2 \ddot{\bf z}_{1}(t)+\dots,\quad\qquad
{\bf z}_{2}(t_2) =  {\bf z}_{2}(t) - {1 \over 2} \dot {\bf z}_{2}(t)+
     {1 \over 8} \tau^2 \ddot{\bf z}_{2}(t)- \dots
\end{equation}
 and integrating over $\tau$ (between $- \infty $ and $ + \infty $),
in the  Coulomb gauge we obtain immediately
\begin{equation}
(i \ln W^{\rm SR})^{(1)} = \int_{t_{\rm i}}^{t_{\rm f}}
{\rm d}t \{ -{4 \over 3} {\alpha_{\rm s} \over r}
[1- {1\over 2}( \delta^{hk} + \hat{r}^h
\hat{r}^k )) \dot{z}_{1}^h \dot{z}_{2}^k + \dots] \}\> ,
\label{eq:otto}
\end{equation}
with ${\bf r}={\bf z}_1 -{\bf z}_2$ and $\hat{\bf r}={{\bf r}/r}$.
If we had  worked, e.g., in the Feynman gauge, we would have obtained
\begin{equation}
(i \ln W^{\rm SR})^{(1)}_{q \bar{q}} =
 \int_{t_{\rm i}}^{t_{\rm f}} {\rm d}t
 \{ -{4 \over 3}
 { \alpha_{\rm s} \over r } [1 - \dot{\bf z}_1 \cdot \dot{\bf z}_2 +
   {1 \over 8} ((\dot{\bf z}_1 + \dot{\bf z}_{2})^2 + {\bf r} \cdot
\ddot{\bf r}) -
{1 \over 8 r^2} (({\bf r}\cdot (\dot{\bf z}_1+\dot{\bf z}_2))^2+\dots
] \}
\label{eq:nove}
\end{equation}
from which  (\ref{eq:otto})
 can be recovered by eliminating the acceleration term by
 partial integration. This is a consequence of
  the gauge invariance of the Wilson
integral.\par
   In a similar way, after renormalization, we can obtain for the
$ \alpha_{\rm s}^2 $ term in the static limit
\begin{equation}
(i \ln W^{\rm {SR}})^{(2)}_{ q \bar{q}}
  = \int_{t_{\rm i}}^{t_{\rm f}} {\rm d}t \, \{-
{4\over 3}{ \alpha_{\rm s}^2 \over
   4 \pi} {1 \over r}[({66-4N_{\rm f} \over 3})(\ln \mu r + \gamma)+A]
+\dots\}.
\label{eq:undici}
\end{equation}
In Eq.(\ref{eq:undici}) $\mu$ is the renormalization scale
 and $A$
 is a constant that depends on the renormalization
 convention. In the $\overline{\rm MS}$ scheme  $A
= {5\over 6}({66-4 N_f\over 3})  -8  $.\par
Let us come to the LR part of the Wilson integral.
 We shall make the assumption
\begin{equation}
i \ln W_{q \bar{q}}^{\rm LR}= \sigma S_{\rm min} +{1\over 2} C P \> ,
\label{eq:dodici}
\end{equation}
where $ S_{\rm min} $ denotes the minimal surface enclosed by the loop $ \Gamma
$ and $ P $ its lenght. Eq. (\ref{eq:dodici})
 is suggested by  the pure lattice gauge
 theory
and it  is believed to be true in the so--called quenched approximation,
i.e. when we replace $ M_{\rm f}(A) $ by 1 in (\ref{eq:due}).
 Corrections to  the pure
potential theory (pair creation effects) should be introduced for this fact but
they shall not be considered here.

In more explicit terms (\ref{eq:dodici}) can be written as
\begin{equation}
  i \ln W^{\rm LR}_{q \bar{q}} = \sigma \, {\rm min}
 \int_{t_{\rm i}}^{t_{\rm f}} {\rm d}t
       \int_0^1 {\rm d}s [-({\partial x \over \partial t})^2 ({\partial x \over
       \partial s})^2 + ({\partial x^{\mu} \over \partial t}{\partial x_{\mu}
       \over \partial s})^2]^{1\over 2}
  + {1 \over 2} C \sum_{j=1,2} \int_{t_{\rm i}}^{t_{\rm f}} {\rm d}t
[{\dot{z}_j^{\mu} \dot{z}_{j \mu}}]^{1\over 2},
\label{eq:tredici}
\end{equation}
where the minimum is taken over all surfaces  of
equation $ x^{\rho}=x^{\rho}(t,\; s) $ having $\Gamma$ as contour.
Obviously $ x^0 = t$,
$ {\bf x}(t,\; 1) = {\bf z}_1 (t)$ and  ${\bf x}(t, \; 0)= {\bf z}_2 (t)$.\par
By solving the appropriate Euler equations and expanding
  in the
velocities, we obtain
\begin{equation}
{\bf x}_{\rm min}(t,\; s) = s \,
 {\bf z}_1 (t) + (1-s)\, {\bf z}_2 (t)
    - {1 \over 2} s (1-s) [{\bf \eta} + {1 \over 3} (1+s) {\bf \zeta}] +
\dots
\label{eq:quindici}
\end{equation}

\noindent with
$
  {\bf \eta}  = (\dot{\bf r}\cdot \dot{\bf z}_2 - {\bf r} \cdot
    \ddot{\bf z}_2) {\bf r} + ({\bf r} \cdot \dot{\bf r}) \dot{\bf z}_2
     - 2 ({\bf r} \cdot \dot{\bf z}_2) \dot {\bf r} + r^2 \ddot{\bf z}_2 $
and
${\bf \zeta} =  - ({\bf r} \cdot \dot{\bf r}) \dot{\bf r} + r^2 \ddot{\bf r}
     + (\dot{r}^2 - {\bf r} \cdot \ddot{\bf r}){\bf r}$.\par
Actually it can be checked that the $ {\rm O} (v^2) $ term
 in (\ref{eq:quindici})
 does not contribute
to $ S_{\rm min} $ at order $v^2$ (such a term is however important in
principle for the evaluation of the functional derivatives).
Replacing (\ref{eq:quindici}) in (\ref{eq:tredici}), finally we have
\begin{eqnarray}
& & \quad  i\ln W^{{\rm LR}}_{q\overline{q}} =
\int_{t_{\rm i}}^{t_{\rm f}} dt \   \sigma r \int_0^1 ds \   [1-(s
\dot{{\bf z}}_{1 \rm T} + (1-s)
 \dot{{\bf z}}_{2 \rm T} )^2]^{\frac{1}{2}} +{1\over 2} C
 \sum_{j=1}^2 \int_{t_i}^{t_f}
 ( 1 - \dot{z}_j^h \dot{z}_j^h)^{1\over 2} =
\nonumber\\
& & =  \int_{t_{\rm i}}^{t_{\rm f}} dt \   \sigma r \
 [ 1-\frac{1}{6}
(\dot{{\bf z}}_{1 \rm T}^2
+ \dot{{\bf z}}_{2 \rm T}^2
+ \dot{{\bf z}}_{1 \rm T} \cdot \dot{{\bf z}}_{2 \rm T} )]
+ \dots
+{1\over 2} C
 \sum_{j=1}^2 \int_{t_i}^{t_f}
 ( 1 -{1\over 2} \dot{z}_j^h \dot{z}_j^h+\dots),
\label{eq:dic}
\end{eqnarray}
where $ \dot{\bf z}_{j {\rm T}}$ denotes the {\it transversal part}
 of $\dot{\bf z}_j $,
$ \dot{z}_{j{\rm T}}^h=  (\delta^{hk} -\hat{r}^h \hat{r}^k)
 \dot{z}_j^h$. \par
 In conclusion, we can write
\begin{equation}
i \ln W_{ q \bar{q}} = ( i \ln W_{ q \bar{q}}^{\rm SR})^{(1)}
+ ( i \ln W_{q \bar{q}}^{\rm SR})^{(2)} + \dots
  + i \ln W_{q \bar{q}}^{\rm LR},
\label{eq:dicbis}
\end{equation}
with the various terms as given by (\ref{eq:otto}), (\ref{eq:undici}),
 (\ref{eq:dic}).\par

Let us turn to the three--quark system. In this
 case  the basic quantity is
\begin{eqnarray}
  W_{3q} = \frac{1}{3!} \left\langle \varepsilon_{a_1 a_2 a_3}
 \varepsilon_{b_1 b_2 b_3}  \left[ {\rm  P} \exp \left( ig
 \int_{\overline{\Gamma}_1} dx^{\mu_1} A_{\mu_1}(x) \right)
\right]^{a_1 b_1} \right.
\nonumber\\
\left. \left[ {\rm P} \exp \left( ig \int_{\overline{\Gamma}_2}
 dx^{\mu_2} A_{\mu_2}(x) \right) \right]^{a_2 b_2}
  \left[  {\rm P} \exp \left( ig \int_{\overline{\Gamma}_3 } dx^{\mu_3}
A_{\mu_3}(x) \right) \right]^{a_3 b_3} \right\rangle \> .
\label{eq:w3}
\end{eqnarray}
\noindent Here $a_j,b_j$ are colour indices, $j=1,2,3$ and
$\overline{\Gamma}_j$  denote the  curve made by:
the world lines $\Gamma_j$ for the  quark $j$
between the times $t_{\rm i}$ and $t_{\rm f}$
($t_{\rm i} < t_{\rm f}$), a straight  line
on the surface $t=t_{\rm i}$ merging from an arbitrary
fixed  point $I$ (which
 we also denote by $y_M$) and connected to
the world line, another  straight line
on the surface $t=t_{\rm f}$ connecting
the world line to a second fixed point $F$ (also denoted  as $x_M$).
\par
Under the  assumptions i) and ii) we can write
in place of (\ref{eq:sex}) and ({\ref{eq:dodici})
\begin{equation}
 i \ln W_{3q} = \frac{2}{3} g^2 \sum _{i<j}
 \int _{\Gamma _i} dx^{\mu}
_i \int _{\Gamma _j} dx^{\nu}_j \  i D_{\mu \nu} (x_i - x_j)
+ \sigma S_{\min} + {1\over 3} C P \> .
\label{eq:diciannove}
\end{equation}
Here the perturbative term is taken at the lowest order in $\alpha_s$
 and $S_{\min}$ denotes the minimum among all
 the surfaces made by three sheets
having the curves $\overline{\Gamma}_1$,
 $\overline{\Gamma}_2$ and $\overline{\Gamma}_3$ as contours and
joining on a line $\Gamma_M$ connecting $I$ with $F$ (the minimum
 is understood at fixed $
\bar{\Gamma}_j$
 as the surfaces and $\Gamma_{\rm M}$ change ).
 Obviously, $P$ denotes the total length of $\bar{\Gamma}_1$,
 $\bar{\Gamma}_2$ and $\bar{\Gamma}_3$.
Notice that a priori the constants $\sigma$ and  $C$
occurring in (17)
 could be  different from those occurring in (\ref{eq:dodici});
 however, the fact that when two quarks coincide
 the potential
 derived from (\ref{eq:diciannove}) must coincide with that derived from
 (\ref{eq:dodici})  ( in a colour singlet
 state two quarks are equivalent to an antiquark) grants that they must be
actually equal.\par
The right--hand  side of (\ref{eq:diciannove})  can be evaluated
 as an expansion  in $\dot{\bf z}_j$  on the same foot used for
 Eqs.(\ref{eq:otto}), (\ref{eq:undici}) and (\ref{eq:dic}). In particular up to
 the second order in the velocities, $ S_{\rm min}$ coincides with the
 surface described by the equations
\begin{equation}
{\bf x}_j^{\rm min} (t,s) =s {\bf z}_j (t) + (1-s) {\bf z}_{M}(t)\> ,
\      \    \    \qquad \qquad  j=1,2,3 \> .
\end{equation}
Here $ {\bf z}_{M} (t)$  is
 constructed from the positions ${\bf z}_1 (t)$, $ {\bf z}_2 (t)$ and
 ${\bf z}_3 (t)$ of the three quarks according to the following rule:
 if no angle in the
triangle   made by ${\bf z}_1 (t)$, $ {\bf z}_2 (t)$ and
 ${\bf z}_3 (t)$ exceeds $120^0$ (configuration I), ${\bf z}_M (t)$
 coincides with the point inside the triangle which sees  the three sides
 under the same angle $120^0$; if one of the three angles in the
triangle  is $\ge 120^0$ (configuration II), ${\bf z}_{M} (t)$
 coincides with the corresponding vertex, let us say ${\bf z}_{\bar{j}}(t)$.
\par
In conclusion, the result is
\begin{eqnarray}
i \ln W_{3q} = \int_{t_{\rm i}}^{t_{\rm f}} dt \   \left\{ \sum_{j<l}
\left[ - \frac{2}{3} \frac{\alpha_s}{r_{jl}} + \frac{1}{2} \frac{2}{3}
\frac{\alpha_s}{r_{jl}} (\delta^{hk} + \hat{r}_{jl}^h \hat{r}_{jl}^k)
\dot{z}_j^h \dot{z}_l^k \right] + \right.
\nonumber\\
\left. {}+ \sigma \sum_{j=1}^{3} r_j \left[ 1-\frac{1}{6}
 (\dot{{\bf z}}_{j{\rm T}_j}^2 + \dot{{\bf z}}^2_{M {\rm T}_j}
+ \dot{{\bf z}}_{j{\rm T}_j} \cdot
\dot{{\bf z}}_{M {\rm T}_j}) \right]
+{C\over 3} \sum_{j=1}^{3} \int_{t_{\rm i}}^{t_{\rm f}}
dt (1 -{1\over 2} \dot{z}_j^h \dot{z}_j^h)
 \right\},
\label{eq:ventidue}
\end{eqnarray}
where  ${\bf r}_{jl} = {\bf r}_j -{\bf r}_l \equiv {\bf z}_j - {\bf
z}_l$, $ {\bf r}_j ={\bf z}_j -{\bf z}_{M}$
 and the transversal prescription ${\rm T}_j$ is now referred
 to ${\bf r}_j$. Furthermore we can notice that
the quantity $\dot{\bf z}_M$ can be obtained by deriving
 the equation $\sum_{j=1}^3 ({\bf r}_j / r_j)=0$. We have
 indeed
 $\sum_{j=1}^3 {1\over r_j} (\delta^{hk} -\hat{r}_j^h
\hat{r}_j^k) \dot{z}_j^k =\sum_{j=1}^3 {1\over r_j} (\delta^{hk} -\hat{r}_j^h
\hat{r}_j^k) \dot{z}_M^k$. Obviously in  configuration II  we
have $\dot{\bf z}_M =\dot{\bf z}_{\bar{j}}$.

\section{Quark--antiquark potential}

The starting point is the gauge invariant quark-antiquark
$(q_1,\bar{q}_2)$ Green function
(for definiteness let us  assume the two  particles
 to have
 different flavours)
\begin{eqnarray}
& & G(x_1,x_2;y_1,y_2) =
\frac{1}{3}\langle0|{\rm T}\psi_2^c(x_2)U(x_2,x_1)\psi_1(x_1)
\overline{\psi}_1(y_1)U(y_1,y_2)  \overline{\psi}_2^c(y_2)
|0\rangle =
\nonumber\\
& &= \frac{1}{3} {\rm Tr} \langle U(x_2,x_1)
 S_1^{{\rm F}}(x_1,y_1|A) U(y_1,y_2) C^{-1}
S_2^{{\rm F}}(y_2,x_2|A) C \rangle \> ,
\label{eq:ventitre}
\end{eqnarray}
where $c$ denotes the charge-conjugate fields, $C$ is the charge-conjugation
matrix, $U$
the path-ordered gauge string
$U(b,a)= {\rm P}  \exp  \left(ig\int_a^b dx^{\mu} \, A_{\mu}(x) \right)$
(the integration path being the straight line joining $a$ to $b$),
 $S_1^{{\rm F}}$ and $S_2^{{\rm F}}$ the quark propagators in an
external gauge field $A^{\mu}$.

We assume $x_1^0=x_2^0=t_{\rm f}$,
$y_1^0=y_2^0=t_{\rm i}$ (with $t_{\rm f}-t_{\rm i} >0$
and large) and
note that $S_j^{{\rm F}}$ are $4\times4$  Dirac type matrices.
Then, performing a Foldy--Wouthuysen transformation on $G$,
we can replace $S_j^{{\rm F}}$ with a Pauli propagator $K_j$ (a
$2\times2$ matrix in the spin indices) and obtain a two-particle
Pauli-type
Green function $K$.
Solving the
Schr\"odinger-like equation for $ K_j$ by the path--integral technique and
 replacing it in the expression of $K$,
 we obtain  even this quantity
 in the form
of a path integral on the world lines of the two quarks
 (see Ref.$^1$ for details):
\begin{eqnarray}
& & K({\bf x}_1, {\bf x}_2, {\bf y}_1, {\bf y}_2; t_{\rm f} - t_{\rm i})=
\int_{{\bf z}_1(t_{\rm i})={\bf y}_1}^{{\bf z}_1(t_{\rm f})={\bf x}_1}
    {\cal D}  [{\bf z}_1, {\bf p}_1]
\int_{{\bf z}_2(t_{\rm i})={\bf y}_2}^{{\bf z}_2(t_{\rm f})={\bf x}_2}
    {\cal D}   [{\bf z}_2, {\bf p}_2]\nonumber \\
& &  \exp \{i\int_{t_{\rm i}}^{t_{\rm f}} dt\,
 \sum_{j=1}^2
[{\bf p}_j \cdot \dot{{\bf z}}_j -m_j-
\frac{{\bf p}^2_j}{2m_j}+\frac{{\bf p}^4_j}{8m_j^3} ]\}
\langle \frac{1}{3}
{\rm Tr \, T_s \, P} \exp \{ig\oint_{\Gamma} dx^{\mu} \,
A_{\mu}(x) \nonumber \\
& & +\sum_{j=1}^2\frac{ig}{m_j} \int_{{\Gamma}_j} dx^{\mu}
  (S_j^l \hat{F}_{l{\mu}}(x) -\frac{1}{2m_j}
S_j^l\varepsilon^{lkr}p_j^k F_{{\mu}r}(x)-
\frac{1}{8m_j} D^{\nu}F_{{\nu}{\mu}}(x)
 ) \}  \rangle \> .
\label{eq:path1}
\end{eqnarray}
Here ${\rm T_s}$ is the time-ordering prescription for the
 spin matrices; P,
 ${\rm Tr}$, $\Gamma$, $\Gamma_1$ and $ \Gamma_2$  are defined as in Eq.(1).
 Furthermore, as usual
$F^{\mu\nu}= \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}
+ ig[A^{\mu},A^{\nu}]$,
$\hat{F}^{\mu\nu}= \frac{1}{2} \varepsilon^{\mu\nu\rho\sigma}
F_{\rho\sigma}$ and
$D^{\nu}F_{\nu\mu}= \partial^{\nu}F_{\nu\mu}+
ig[A^{\nu},F_{\nu\mu}]\>$,
 $\varepsilon^{\mu\nu\rho\sigma}$ being the four-dimensional Ricci
symbol. \par
In order to show that the interaction between $q_1$ and $\bar{q}_2$
 can be described in terms of a semirelativistic potential
 we must check that at the order $ {1\over m^2}$ we can write
\begin{equation}
\left\langle \frac{1}{3}
{\rm Tr \, T_s \, P} \exp \ldots\right \rangle =
{\rm T_s} \exp\left[ -i\int_{t_{\rm i}}^{t_{\rm f}} dt \,
 V^{q\overline{q}}({\bf z}_1(t),{\bf
z}_2(t),{\bf p}_1(t),{\bf p}_2(t),{\bf S}_1,{\bf S}_2) \right] \> ,
\label{eq:ventinove}
\end{equation}
for some
$V^{q\overline{q}}$.
Expanding the logarithm on the left-hand side of (\ref{eq:ventinove}),
this is equivalent to state
\begin{eqnarray}
 i \ln W_{q\overline{q}}  +
i \sum_{j=1}^2 \frac{ig}{m_j} \int_{{\Gamma}_j}dx^{\mu}
\bigg( S_j^l \, \langle\langle \hat{F}_{l\mu}(x)
 \rangle \rangle -\frac{1}{2m_j} S_j^l
 \varepsilon^{lkr} p_j^k \, \langle\langle
F_{\mu r}(x) \rangle\rangle -
\nonumber\\
{} - \frac{1}{8m_j} \, \langle\langle
D^{\nu} F_{\nu\mu}(x) \rangle\rangle \bigg)
 - \frac{1}{2} \sum_{j,j^{\prime}} \frac{ig^2}{m_jm_{j^{\prime}}}
{\rm T_s} \int_{{\Gamma}_j} dx^{\mu} \, \int_{{\Gamma}_{j^{\prime}}}
dx^{\prime\sigma}
\, S_j^l \, S_{j^{\prime}}^k
\nonumber\\
\bigg( \, \langle\langle \hat{F}_{l \mu}(x)
 \hat{F}_{k \sigma}(x^{\prime})
\rangle\rangle - \, \langle\langle \hat{F}_{l \mu}(x) \rangle\rangle
\, \langle\langle \hat{F}_{k \sigma}(x^{\prime}) \rangle\rangle \bigg)
 +\dots =\left[\int_{t_{\rm i}}^{t_{\rm f}} dt
 \, V^{q\overline{q}} \right] \> ,
\end{eqnarray}
with the notation
\begin{equation}
\langle\langle f[A] \rangle\rangle = \frac{\frac{1}{3} \left\langle
{\rm Tr \, P}\left[ \exp ( ig\oint_{\Gamma}dx^{\mu}
 \, A_{\mu}(x) ) \right] f[A]
\right\rangle}
{\frac{1}{3} \left\langle {\rm Tr \, P}  \exp ( ig\oint_{\Gamma} dx^{\mu}
\, A_{\mu}(x) ) \right\rangle}
\end{equation}
and $W_{q\overline{q}}$ as given by (\ref{eq:dicbis}).\par
 Notice that after replacing $\dot{\bf z}_j$ by $ {{\bf p}_j \over m_j}$
 in Eqs.(\ref{eq:otto}), (\ref{eq:undici}) and (\ref{eq:dic}),
 the expression resulting for
  $ i \ln W_{ q \bar{q}}$
 is already of the desired form. Concerning the  spin--dependent part
 we observe that the occurring field expectation values  can
 be expressed in terms of $ i \ln W_{q \bar{q}}$ by the functional derivatives
\begin{equation}
g \, \langle \langle F_{\mu\nu}(z_1) \rangle \rangle =
\frac{ \delta (i \ln W_{q\overline{q}}) }
{ \delta S^{\mu\nu}(z_1)} \>,
\label{eq:trentatre}
\end{equation}

\begin{eqnarray}
g^2 \, \bigg( \langle \langle F_{\mu\nu}(z_1)
F_{\rho\sigma}(z_2) \rangle \rangle
& -& \langle \langle F_{\mu\nu}(z_1) \rangle \rangle \,
\langle \langle F_{\rho\sigma}(z_2)  \rangle \rangle \bigg) =
\nonumber\\
& = &\frac{ \delta^2 \ln W_{q\overline{q}}}
{\delta S^{\mu\nu}(z_1) \delta S^{\rho\sigma}(z_2)}
 =  - ig \frac{\delta}{\delta S^{\rho\sigma}(z_2)}
\, \langle \langle F_{\mu\nu}(z_1) \rangle \rangle ,
\label{eq:trentaq}
\end{eqnarray}
where $ \delta S^{\mu \nu} (z_j) ={1\over 2} ( d z_j^{\mu} \delta z_j^{\nu}
 - d z_j^{\nu} \delta z_j^{\mu})$ is the element of the  surface  spanned
 by the path $ z_j(t)$ as a consequence of the variation
 $ z_j (t) \to z_j (t) +\delta z_j (t)$.\par
The evaluation of the right hand side of (\ref{eq:trentatre})
 and (\ref{eq:trentaq}) requires some care, since the functional
 derivatives may lower the order of magnitude in the velocities.
 However, it
 can be done  without any additional
 assumptions and the results are
\begin{equation}
g \, \langle\langle F_{0k}(z_1) \rangle\rangle =
( \frac{4}{3} \alpha_s \frac{1}{r^3}+ \frac{\sigma}{r}) r^k
+ O(v^2)\> ,
\end{equation}
\begin{equation}
g \, \langle\langle F_{hk}(z_1) \rangle\rangle =
 (\frac{4}{3} \frac{\alpha_s}{m_2} \frac{1}{r^3}
+ \frac{\sigma}{m_2} \frac{1}{r} )
( r^h p_2^k - r^k p_2^h ) +O(v^3) \> ,
\end{equation}
\begin{eqnarray}
& & g^2 \, \bigg( \langle\langle F_{hk}(z_1) F_{lm}(z_2) \rangle\rangle -
\langle\langle F_{hk}(z_1) \rangle\rangle \,
\langle\langle F_{lm}(z_2) \rangle\rangle \bigg)  =
\nonumber\\
& &= - \frac{4}{3} \frac{ig^2}{8\pi} \delta (t_1-t_2) \left\{
\partial_l \partial_k \left[ \frac{1}{r} \left( \delta^{hm}
+ \hat{r}^h \hat{r}^m \right)\right] - \partial_l \partial_h \left[
\frac{1}{r} \left( \delta^{km} + \hat{r}^k
 \hat{r}^m \right) \right]
- \right.
\nonumber\\
& &\left. - \partial_m \partial_k \left[ \frac{1}{r} \left(
\delta^{hl} + \hat{r}^h \hat{r}^l \right)\right] + \partial_m
\partial_h \left[ \frac{1}{r} \left( \delta^{kl} + \hat{r}^k
\hat{r}^l \right)\right] \right\} + O(v^2)\> ,
\end{eqnarray}

\begin{equation}
\bigg( \langle\langle F_{\mu\nu}(z_1) F_{\rho\sigma}(z_1')
\rangle\rangle - \langle\langle F_{\mu\nu}(z_1) \rangle\rangle \,
\langle\langle F_{\rho\sigma}(z_1') \rangle\rangle \bigg)
=0
\end{equation}
and similar ones. \par
In the end one obtains the potential in the form  of a static part,
a spin--dependent part  and a velocity--dependent one,
$ V^{q\overline{q}} = V^{q\overline{q}}_{{\rm stat}} +
V^{q\overline{q}}_{{\rm sd}} +
V^{q\overline{q}}_{{\rm vd}}$,
with
\begin{equation}
V^{q\overline{q}}_{{\rm stat}} = -  \frac{4}{3}
 \frac{{\alpha}_s}{r} + \sigma r -{4\over 3} {\alpha_{\rm s}^2 \over 4 \pi}
 {1\over r} [{66- 4 N_{f} \over 3}
 (\ln \mu r + \gamma) +A]
\label{eq:trena}
\end{equation}
\begin{eqnarray}
& & V^{q\overline{q}}_{{\rm sd}} =
\frac{1}{8} \sum_{j=1,2} {1\over m_j^2}
\nabla^2 \left( - \frac{4}{3} \frac{\alpha_s}{r} + \sigma r \right)
+
   \left(
 \frac{4}{6} \frac{\alpha_s}{r^3} -
\frac{\sigma}{2 r} \right) \sum_{j=1,2} \frac{1}{m_j^2} {\bf S}_j \cdot
{\bf L}_j
 + \frac{1}{m_1m_2} \frac{4}{3} \frac{\alpha_s}{r^3}\nonumber \\
& & ({\bf S}_2
\cdot{\bf L}_1  + {\bf S}_1 \cdot{\bf L}_2 ) +
 {4 \alpha_{\rm s}\over 3 m_1 m_2} \left [
 (\frac{3}{r^5} ({\bf S}_1 \cdot {\bf r})({\bf S}_2 \cdot
{\bf r}) - {{\bf S}_1 \cdot {\bf S}_2\over r^3}) +
\frac{8\pi}{3} \delta^3({\bf r}) {\bf S}_1 \cdot {\bf S}_2 \right ]
\label{eq:trenb}
\end{eqnarray}

\begin{eqnarray}
V_{\rm vd}^{q \bar{q}} & =& {1\over m_1 m_2} \{ {4\over 3}
 {\alpha_s \over r} ( \delta^{hk}+ \hat{r}^h \hat{r}^k)
 p_1^h p_2^k \}_{\rm Weyl} - C \sum_j {p_j^2 \over 4 m_j^2} \nonumber \\
& -& \sum_{j=1}^2 {1\over 6 m_j^2} \{ \sigma r {\bf p}_{j {\rm T}}
\}_{\rm Weyl} -{1\over 6 m_1 m_2} \{ \sigma r {\bf p}_{1 {\rm T}}
 \cdot {\bf p}_{2 {\rm T}} \}_{\rm Weyl}.
\label{eq:trenc}
\end{eqnarray}

At  the order $ \alpha_s$ the above  potential
 coincides globally  with that given in Ref.$^1$. In particular
$V_{\rm sd}$
 was  originally given by Eichten and Feinberg  and corrected by
 Gromes$^2$ (see also Ref.$^3$), while $V^{\rm vd}$
  has been obtained for the first time in$^1$.
Notice  that Eq.(\ref{eq:trenc}) differs from the
 corresponding one
   proposed under the ad hoc assumption
 of scalar confinement and does not present the phenomenological
 difficulties of this $^7$. Notice also that the terms in $C$ can
 be reabsorbed in a redefinition of the masses $m_j\to m_j'=
m_j+{C\over 2}$.
 The $O(\alpha_s^2)$ term in
 (\ref{eq:trena}) has been obtained for the first time in $^6$.\par
The  $ O(\alpha_s^2)$ contributions to $V_{\rm sd}$
 and $V_{\rm vd}$  have been evaluated by Gupta et al.$^8$
 in an $S$ matrix  context  but they  have not been
 included here.
 In fact  such contributions
 are found to be important for an understanding of the fine and hyperfine
 structure  of the meson spectrum. However, due to the ambiguities inherent
  in the derivation method, a consistent evaluation in the Wilson loop
 approach should be desirable. Calculations are in progress
 in this line.\par
Finally, let us come to the ordering   in (\ref{eq:trenc}).
 Obviously, ordering is related to the discretization prescription
 in the definition of the path integral. If in the definition
of the gauge field functional integration we identify  the element
 $U_{n' n}$ of the colour group associated to the link between
 the contiguous sites $n$ and $n'$ with $\exp{ [ig (x_{n'}-x_{n})^{\mu}
 A_{\mu} ({x_{n'}+ x_{n} \over 2})]}$, we obtain the Weyl ordering
\begin{eqnarray}
& & \quad \quad \{ X^{hk}(r), p^h_j p^k_{j\prime} \}_{\rm Weyl} = {1\over 4}
 \{p^h_j, \{ X^{hk}(r), p^k_{j\prime}\} \}=\nonumber \\
& & = {1\over 4} ( X^{hk} (r) p^h_j p^k_{j\prime}+
   p^h_j X^{hk}(r) p^k_{j\prime} +  p^k_{j\prime} X^{hk} (r) p^h_j +
 X^{hk} (r) p^h_j p^k_{j\prime}).
\label{eq:ordering}
\end{eqnarray}

\section{Three-quark potential}

The three-quark
 gauge invariant Green function  can be written as
(again we assume the quarks to have differents flavours)
\begin{eqnarray}
& & \qquad   \qquad \quad \quad G(x_1,x_2,x_3,y_1,y_2,y_3)
 = \frac{1}{3!} \varepsilon_{a_1 a_2 a_3}
\varepsilon_{b_1 b_2 b_3}
\nonumber\\
& &\langle 0| {\rm T} \,
U^{a_3 c_3}(x_M,x_3) U^{a_2 c_2}(x_M,x_2)
 U^{a_1 c_1}(x_M,x_1)
\psi_{3 c_3}(x_3)
\psi_{2 c_2}(x_2) \psi_{1 c_1}(x_1)
\nonumber\\
& &\overline{\psi}_{1 d_1}(y_1) \overline{\psi}_{2 d_2}(y_2)
\overline{\psi}_{3 d_3}(y_3)
U^{d_1 b_1}(y_1,y_M) U^{d_2 b_2}(y_2,y_M)
 U^{d_3 b_3}(y_3,y_M)
 |0 \rangle
\label{eq:gtre}
\end{eqnarray}
and we assume
 $x_1^0=x_2^0=x_3^0= x_M^0= t_{\rm f}$,
$y_1^0=y_2^0=y_3^0= y_M^0=t_{\rm i}$,
$  t_{\rm f}- t_{\rm i}$ large.

The integration over the fermionic variables is again trivial
 and one can write
\begin{eqnarray}
G({\bf x}_1, {\bf x}_2, {\bf x}_3, {\bf y}_1, {\bf y}_2,
{\bf y}_3; \tau)
 = \frac{1}{3!} \varepsilon_{a_1 a_2 a_3}
\varepsilon_{b_1 b_2 b_3} \bigg\langle \bigg( U(x_M,x_1)
S_1^{\rm F}(x_1,y_1|A) U(y_1,y_M) \bigg)^{a_1 b_1}
\nonumber\\
\bigg( U(x_M,x_2) S_2^{\rm F}(x_2,y_2|A)
 U(y_2,y_M) \bigg)^{a_2 b_2}
\bigg( U(x_M,x_3) S_3^{\rm F}(x_3,y_3|A)
 U(y_3,y_M) \bigg)^{a_3 b_3}
\bigg\rangle \> .
\label{eq:treprop}
\end{eqnarray}

{}From (\ref{eq:treprop}),
we can proceed  strictly as in Sec.3 and
in conclusion we have to show that
\begin{eqnarray}
 i \ln W_{3q}  +
i \sum_{j=1}^3 \frac{ig}{m_j} \int_{{\Gamma}_j}dx^{\mu}
\bigg( S_j^l \, \langle\langle \hat{F}_{l\mu}(x)
 \rangle \rangle -\frac{1}{2m_j} S_j^l
 \varepsilon^{lkr} p_j^k \, \langle\langle
F_{\mu r}(x) \rangle\rangle -
\nonumber\\
{} - \frac{1}{8m_j} \, \langle\langle
D^{\nu} F_{\nu\mu}(x) \rangle\rangle \bigg)
 - \frac{1}{2} \sum_{j,j^{\prime}} \frac{ig^2}{m_jm_{j^{\prime}}}
{\rm T_s} \int_{{\Gamma}_j} dx^{\mu}
\, \int_{{\Gamma}_{j^{\prime}}}
dx^{\prime\sigma}
\, S_j^l \, S_{j^{\prime}}^k \cdot
\nonumber\\
\cdot \bigg( \, \langle\langle \hat{F}_{l \mu}(x)
 \hat{F}_{k \sigma}(x^{\prime})
\rangle\rangle - \, \langle\langle \hat{F}_{l \mu}(x) \rangle\rangle
\, \langle\langle \hat{F}_{k \sigma}(x^{\prime}) \rangle\rangle \bigg)
 =  \left[\int_{t_{\rm i}}^{t_{\rm f}} dt
 \, V^{3q}({\bf z}_j, {\bf p}_j, {\bf S}_j) \right]
\end{eqnarray}
with  $W_{3q}$ given by (\ref{eq:ventidue}) and
\begin{equation}
\langle\langle f[A] \rangle\rangle= \frac{ \frac{1}{3!} \langle
\varepsilon \varepsilon \, \{ \prod_j \, {\rm P}
[ \exp (ig \int_{\overline{\Gamma}_j} dx^{\mu}
\, A_{\mu}(x) )] \} f[A] \rangle }{\frac{1}{3!} \langle \varepsilon
\varepsilon \, \{ \prod_j \, {\rm P} \exp
(ig \int_{\overline{\Gamma}_j} dx^{\mu} \, A_{\mu}(x)
) \} \rangle } \> .
\end{equation}
Again, after the replacement $ \dot{{\bf z}}_j \to {\bf p}_j/m_j$,
the quantity  $ i \ln W_{3 q}$  is
 already of the desired form, while  the field expectation values
 can be evaluated according to equations analogues to (\ref{eq:trentatre})
 and (\ref{eq:trentaq}) and lead to similar expressions.
The final result is again of the form
$ V^{3q} = V^{3q}_{{\rm stat}} + V^{3q}_{{\rm sd}} +
V^{3q}_{{\rm vd}}$
with
\begin{eqnarray}
V^{3q}_{{\rm stat}} & =&
\sum_{j<l} \left( -\frac{2}{3}
\frac{\alpha_s}{r_{jl}} \right) + \sigma (r_1+r_2+r_3)+
C,
\label{eq:trestat}\\
V^{3q}_{{\rm sd}} & = &
\frac{1}{8m_1^2} \nabla^2_{(1)} \left( -\frac{2}{3}
\frac{\alpha_s}{r_{12}} -\frac{2}{3} \frac{\alpha_s}{r_{31}} +
\sigma r_1 \right) +
\nonumber\\
{}&+& \left\{ \frac{1}{2m_1^2} {\bf S}_1 \cdot \left[
({\bf r}_{12} \times {\bf p}_1) \left( \frac{2}{3}
\frac{\alpha_s}{r_{12}^3} \right) + ({\bf r}_{31} \times
{\bf p}_1) \left( -\frac{2}{3} \frac{\alpha_s}{r_{31}^3}
\right) - \frac{\sigma}{r_1} ({\bf r}_1 \times {\bf p}_1)
\right]  \right. +
\nonumber\\
{} &+& \left. \frac{1}{m_1m_2} {\bf S}_1 \cdot ({\bf r}_{12}
\times {\bf p}_2) \left( -\frac{2}{3} \frac{\alpha_s}{r_{12}^3}
\right) + \frac{1}{m_1m_3} {\bf S}_1 \cdot ({\bf r}_{31}
\times {\bf p}_3) \left( \frac{2}{3} \frac{\alpha_s}{r_{31}^3}
\right) \right\} +
\nonumber\\
{} &+&
 \frac{1}{m_1m_2} \frac{2}{3} \alpha_s \left\{
\frac{1}{r_{12}^3} \left[ \frac{3}{r_{12}^2} ({\bf S}_1
\cdot {\bf r}_{12}) ({\bf S}_2 \cdot {\bf r}_{12}) -
{\bf S}_1 \cdot {\bf S}_2 \right] + \frac{8\pi}{3}
\delta^3 ({\bf r}_{12}) {\bf S}_1 \cdot {\bf S}_2
\right\}  +
\nonumber\\
{} &+& \, \mbox{cyclic permutations} \> ,
\label{eq:tresd}
\end{eqnarray}
\begin{eqnarray}
V^{3q}_{{\rm vd}} &=&
 \sum_{j<l} \frac{1}{2m_jm_l} \left\{ \frac{2}{3}
\frac{\alpha_s}{r_{jl}} (\delta^{hk} + \hat{r}_{jl}^h \hat{r}_{jl}^k)
p_j^h p_l^k \right\}_{{\rm Weyl}} -
\sum_{j=1}^{3} \frac{1}{6m_j^2} \{ \sigma \, r_j \,
 {\bf p}_{j{\rm T}_j}^2 \}_{{\rm Weyl}} -
\nonumber\\
{} &-& \sum_{j=1}^{3} \frac{1}{6} \{ \sigma \, r_j \,
 \dot{{\bf z}}_{M{\rm T}_j}^2 \}_{{\rm Weyl}} -
\sum_{j=1}^{3} \frac{1}{6m_j} \{ \sigma \, r_j \,
 {\bf p}_{j{\rm T}_j} \cdot \dot{{\bf z}}_{M{\rm T}_j} \}_{{\rm Weyl}}
- \sum_{j} {C \over  6 m_j^2} p^2_j,
\>
\label{eq:trevd}
\end{eqnarray}
where the notations are the same as used in (\ref{eq:ventidue})
 and the ordering is as in (\ref{eq:ordering}).
Notice, in particular, that
 the quantity $\dot{{\bf
z}}_{M}$
 in (\ref{eq:trevd}) is given by
\begin{equation}
 \dot{\bf z}_{M} = \left\{
\begin{array} {ll}
R^{-1} \sum_{j=1}^3 \left( {\bf p}_{j {\rm T}_j}/m_j r_j   \right)
\qquad \mbox{ type I configuration}& \\
{\bf p}_{\bar{j}}/m_{\bar{j}} \qquad \qquad
\qquad \qquad \quad \mbox{ type II configuration}:
({\bf z}_M\equiv{\bf z}_{\bar{j}}) \> ,
\end{array} \right.
\end{equation}
$R$ being the matrix with elements $R^{hk}= \sum_{j=1}^3 \frac{1}{r_j}
(\delta^{hk} -\hat{r}^h_j \hat{r}^k_j)$.

Notice  that Eq.(\ref{eq:tresd}) properly refers to   the configuration
I case.
 In general one should write $
V_{\rm sd}^{\rm LR}= - \sum_{j=1}^3 {1 \over 2 m_j^2}
 {\bf S}_j \cdot {\bf \nabla}_{j} V_{\rm stat}^{\rm LR} \times
 {\bf p}_j $
(In comparing this with (\ref{eq:tresd})
 one should keep in mind that the
partial derivatives in ${\bf z}_M$ of
$V_{\rm stat}^{\rm LR}$ vanish due to the definition of $M$).

We observe that
the short range part in Eqs.(\ref{eq:trestat})--(\ref{eq:trevd})
 is of  a  pure two body
type: in fact it is identical to the electromagnetic
 potential among three equally charged
particles but for the colour group factor $2/3$ and
it is well known. Even the static
confining potential in Eq.(\ref{eq:trestat}) is well  known
(for a review see e.g.$^9$).
Furthermore the long range part  in
Eq.(\ref{eq:tresd}) coincides with the expression obtained by Ford$^{10}$
 starting
from the assumption of a purely scalar Salpeter potential of the form
\begin{equation}
 \sigma \, (r_1 + r_2 + r_3) \, {\beta}_1 {\beta}_2 {\beta}_3 \> ,
\label{eq:fordbs}
\end{equation}
but to our knowledge it was not  obtained consistently in a
Wilson loop context before Ref.$^1$. Eq.(\ref{eq:trevd}) has
been given for the first time in Ref.$^1$. Eq. (\ref{eq:trevd})
differs from  the corresponding equation obtained from (\ref{eq:fordbs}).
The situation for  the three quarks is so similar to that occurring for
 the quark--antiquark system. In Eqs.(39) and (41) the terms in $C$
 can be again eliminated by  the redefinition of the masses
 $m_j\to m_j''=m_j+{C\over 3}$. Notice however  that $m_j''$ differs
 from $m_j'$.

\section{ Relativistic flux tube model}

Let us now neglect in Eq.(\ref{eq:path1}) the spin--dependent terms
 and replace the ${1\over m^2}$ expansion by its exact relativistic
 expression
\begin{eqnarray}
& &K({\bf x}_1, {\bf x}_2;  {\bf y}_1, {\bf y}_2; t_{\rm f} - t_{\rm i}) =
\nonumber \\
& &\int {\cal D} [{\bf z}_1, {\bf p}_1]
\int {\cal D} [{\bf z}_2, {\bf p}_2]
\exp \left\{i \left[ \int_{t_{\rm i}}^{t_{\rm f}} dt \sum_{j=1}^2 ({\bf p}_j
\cdot {\dot{\bf z}_j} - \sqrt{m_j^2 + {\bf p}_j^2})
\right] + \ln W_{q \bar{q}} \right\} .
\label{eq:alfa}
\end{eqnarray}
Let us further evaluate $ i \ln W_{ q \bar{q}}^{\rm SR}$ by the original
   Eq.(\ref{eq:sex}) and assume that a sensible
 approximation is obtained even in the  relativistic case postulating
  the first line  of Eq.(\ref{eq:dic}) in the center--of--mass system
 of the two particles. Then, if we expand again the exponent in
 (\ref{eq:alfa}) around the stationary values ${\bf p}_j = { m {\bf z}_j
\over \sqrt{1-{\bf z}^2_j}}$, in the gaussian approximation
we obtain the ordinary  lagrangian
\begin{eqnarray}
 L  & & = - \sum_{j=1}^2 m_j \sqrt{1- \dot {\bf z}_j^2 } +
 {4 \over 3} { {\alpha}_s  \over r} \left[ 1 - \frac{1}{2}
( \delta^{hk} + \hat{r}^h \hat{r}^k ) \dot{z}_1^h \dot{z}_2^k \right]
+\nonumber \\
 & & {} - \sigma
r \int_0^1 ds [1 - ( s \dot{\bf z}_{1{\rm T}} + (1-s) \dot{{\bf
z}}_{2{\rm T}} )^2 ]^{1/2}.
\label{eq:beta}
\end{eqnarray}
This coincides with the relativistic flux--tube lagrangian$^{11}$.\par
 From (\ref{eq:beta}) is not possible to obtain even a classical
 hamiltonian in a closed form, due to the complicate velocity dependence.
However, in terms of an expansion in ${\sigma \over m^2}$ we have  ( we
 assume $m_1=m_2=m$ for simplicity  and have already  eliminated
 the terms in $C$)
\begin{eqnarray}
{\cal{H}}({\bf r}, {\bf q})& = &2 \sqrt{m^2+q^2} +{\sigma r\over 2}
 \Big [{\sqrt{m^2+q^2}\over q_{\rm T}}\, {\rm arcsin}{q_{\rm T}
 \over \sqrt{m^2+q^2}}
+\sqrt{{m^2+ q_{\rm r}^2\over m^2+q^2}}\Big ]+\nonumber \\
& +&{\sigma^2 r^2 \over 16 q_{\rm T}^2} {m^2+ q_{\rm r}^2 \over \sqrt{m^2+q^2}}
\Big  [ {\sqrt{m^2+q^2} \over q_{\rm T}}\,  {\rm arcsin} {q_{\rm T}
 \over \sqrt{m^2+q^2}}
-\sqrt{{m^2+q_{\rm r}^2\over m^2+q^2}}\Big ]^2 + \dots
\label{eq:gamma}
\end{eqnarray}
with ${\bf r}= {\bf z}_{1{\rm CM}}- {\bf z}_{2{\rm CM}}$,
${\bf q}={\bf p}_{1 {\rm CM}}=-{\bf p}_{2 {\rm CM}}$, ${\bf q}_{\rm r}=
(\hat{\bf r}\cdot {\bf q})/ {\hat{\bf r}}$ and  $q^h_{\rm T}= (\delta^{hk}
 -\hat{r}^h \hat{r}^k ) q^k$.
{}From this a quantum hamiltonian can  be immediately obtained
 by setting
\begin{equation}
 \langle  {\bf k}' \vert H_{\rm FT} \vert {\bf k}\rangle=
 \int {{\rm d}{\bf r} \over (2 \pi)^3} e^{i ({\bf k}-{\bf k}')
\cdot {\bf r}} \,\,
 {\cal {H}}({\bf r}, {{\bf k}'+
{\bf k}\over 2}),
\label{eq:delta}
\end{equation}
in which the ordering prescription is again Weyl prescription.
 By an expansion in ${1\over m^2}$ a semirelativistic
 hamiltonian  can be obviously reobtained with a potential
 given by (\ref{eq:trena})--(\ref{eq:trenc}).

\section{ Bethe--Salpeter equation}

Let us go back  to the
equation analogous to (\ref{eq:ventitre})
 for spinless quarks
 and  in it use  the covariant representation for the quark propagator
 in an external gauge field
\begin{equation}
\Delta^{\rm F} (x,y\vert A)={- i\over 2} \int_0^{\infty} d \tau
 \int_{z(0)=y}^{z(\tau)=x} {\cal D} [z] {\rm P}
{\rm exp}\,  i\int_0^{\tau} {\rm d} \tau\prime \{ -{1\over 2}
 [ ({d z \over d \tau\prime})^2 +m^2] - g z^{\mu}\prime A_{\mu} (z) \}
\label{eq:prop}
\end{equation}

 In place of (\ref{eq:path1})
 we find
\begin{eqnarray}
& &
G_4(x_1,x_2; y_1, y_2) =({-i\over 2})^2 \int_0^{\infty} d\tau_1
\int_0^{\infty} d\tau_2 \int_{z_1(0)=y}^{z_1(t_1)=x_1} {\cal
 D}[z_1] \int_{z_2(0)=y_2}^{z_2(\tau_2)=x_2} {\cal D} [z_2]
\nonumber \\
& & {\rm exp} {-i \over 2} \{ \int_0^{\tau_1} d \tau_1' [
 ({d z_1\over d\tau_1'})^2 + m_1^2 ] + \int_0^{\tau_2} d \tau_2'
 [ ({d z_2\over  d\tau_2'})^2 +m_2^2 ]\}
\cdot {1\over 3} \langle  {\rm Tr}\, {\rm P}\,
 {\rm exp}\, ig \oint d z^{\mu} A_{\mu} (z) \rangle
\nonumber \\
& & \quad \quad \quad
\label{eq:g4bs}
\end{eqnarray}
where  the equation of a path
 connecting $y$ with $x$ is written as
$ z^{\mu} = z^{\mu}(\tau) $,
 in terms of an arbitrary parameter
 $\tau$ (rather than   the time $t$)
 and $z'$ stands for $z(\tau')$.
Notice the occurrence again  in (\ref{eq:g4bs}) of the Wilson loop
 integral $W_{q \bar{q}}$. Even in this case we can use the
 evaluation  of $ i \ln W_{q \bar{q}}^{\rm SR} $ as given by Eq.
 (\ref{eq:cinque}) or (\ref{eq:sex})
 and assume  for  $i \ln W_{q \bar{q}}^{\rm LR}$
 the first line of (\ref{eq:dic}) in the center--of--mass system.\par
Then, by appropriate manipulations of the resulting expression,
 one can obtain the Bethe--Salpeter equation
\begin{eqnarray}
& & G_4(x_1, x_2; y_1, y_2)  =  G_2(x_1-y_1)\,  G_2(x_2-y_2)
 + \int  d^4 \xi_1 d^4 \xi_2 d^4 \eta_1 d^4 \eta_2 \nonumber \\
& & G_2(x_1-\xi)\, G_2(x_2-\xi_2)\, I(\xi_1 ,\xi_2; \eta_1 ,\eta_2)
 \, G_4 (\eta_1,\eta_2; y_1, y_2),
\label{eq:bseq}
\end{eqnarray}
with a kernel of the form
$ I(\xi_1, \xi_2;\eta_1, \eta_2)= I^{\rm SR} (\xi_1, \xi_2;
 \eta_1, \eta_2) + I^{\rm LR}(\xi_1, \xi_2;
 \eta_1, \eta_2)$.
Here $I^{\rm SR}$ coincides with  the ordinary  perturbative
 kernel, while in the momentum representation
 $I^{\rm LR}$  can be written as  (for simplicity we have
 neglected the perimeter term)
\begin{equation}
\tilde{I}^{\rm LR} (p_1', p_2'; p_1,p_2)  =
 {1\over (2 \pi)^3} \int d^3 {\bf r} e^{i ({\bf k}'- {\bf k})\cdot
 {\bf r}}  J({\bf r}, { { p}^{'}_1+p_1 \over 2},
 { p_2'+p_2 \over 2})
\label{eq:bsform}
\end{equation}
($p_1\prime +p_2\prime= p_1 +p_2 ,\,  {\bf p}_1= - {\bf p}_2= {\bf k}$,
 $ {\bf p}_1\prime= - {\bf p}_2\prime={\bf k}\prime $) with
\begin{eqnarray}
J({\bf r}, q_1, q_2)& = & (2 \pi)^3 {\sigma r \over 2}
 {1\over q_{10} +q_{20}} [ q_{20}^2 \sqrt{ q_{10}^2 -{\bf q}_{\rm T}^2}
+ q_{10}^2  \sqrt{q_{20}^2 -{\bf q}^2_{\rm T}} +\nonumber \\
& +& { q_{10}^2 q_{20}^2 \over \vert {\bf q}_{\rm T}\vert }
 ( {\rm arcsin }{ \vert {\bf q}_{\rm T} \vert \over
 \vert q_{10}\vert } + {\rm arcsin } { \vert {\bf q}_{\rm T}\vert
 \over \vert q_{20}\vert } )] + O({\sigma^2 \over m^4})
\label{eq:kerndef}
\end{eqnarray}
(having set ${\bf q}_1= -{\bf q}_2={\bf q}$, $ q^h_{\rm T}=
 (\delta^{hk} -\hat{r}^h \hat{r}^k ) q^k$).\par
Notice that, according to a standard procedure, the BS kernel
 $\tilde{I}$  can be associated  with a relativistic potential
 (to be used in the Salpeter equation) given by
\begin{equation}
\langle {\bf k}' \vert V \vert {\bf k} \rangle ={1\over
 (2 \pi)^3} { m_1 m_2 \over \sqrt{ w_1({\bf k}) w_2({\bf k})
 w_1({\bf k}') w_2({\bf k}')}} \tilde{I}_{\rm inst} ({\bf k}', {\bf k})
\end{equation}
where $w_j({\bf k})= \sqrt{m_j^2+{\bf k}^2}$
 and the instantaneous kernel $ \tilde{I}_{\rm inst}$ is obtained
 from $\tilde{I}$ by setting $p_{10}, p_{20}$ and $ p_{10}', p_{20}'$
 equal to appropriate functions of ${\bf k}$ and ${\bf k}'$,
 respectively. In the present case it is convenient to choose
 $ p_{10}=p_{10}'=\sqrt{w_1({\bf k}) w_2({\bf k}')}$ ,
 $p_{20}=p_{20}'=\sqrt{w_1({\bf k}) w_2({\bf k}')}$. If we do so
 we reobtain the Hamiltonian (\ref{eq:delta}).\par
Going back to the expression of the  kernel  $\tilde{I}^{\rm LR}$
  as given by (\ref{eq:kerndef})--(\ref{eq:bsform}),
 one has to notice that this is
 highly  singular  for $ {\bf k}'= {\bf k}$,
 due to the occurrence of the factor
 $ r$ in  (\ref{eq:kerndef}), and it must be appropriately regularized
  before being used in equation (\ref{eq:bseq}) (e.g., one can make
 the substitution $ r\to r e^{-\varepsilon r}$).
 This circumstance  is related to the fact that,
 being confining, $\tilde{I}^{\rm LR}$
   should admit only bound states, while the
 inhomogeneous BS equation provides also a continuous  two--particles spectrum.
 Therefore one should solve (\ref{eq:bseq}) for the regularized
 kernel and only  at the end take the limit
 for $\varepsilon \to 0 $ (we admit
 in this way that  resonances would evolve in bound states).

\section{Acknowledgements}
We acknowledge warmly  Prof. E.Montaldi and Dr. P.Consoli
 for having contributed
 to some of the results reported in this paper.

\section{References}

redpajama_set_name: RedPajamaArXiv


Heads-up, privacy compliance. WNYC's On the Media looks at the recently passed California SB-178 electronic privacy regulation, and its implications for consumers and information technology providers. For example, police will need a warrant in some circumstances where they previously had unfettered access to cell phone data.


text:
Crosswalk recordings offer positive messages
Tim Dye, a California artist-inventor, retooled a crosswalk "wait/walk" button to offer upbeat messages from people he met traveling across America.
Push to Change World, by Tim DyeArtist-technologist Tim Dye redesigned several downtown Petaluma, California crosswalk stations to play crowd-sourced brief, inspiring messages with the push of a button. Photo by Tim Dye.
When you press a button at a crosswalk, what you hear ("Main Street. Wait! Wait! Wait!" followed by "Walk" or that beeping or rattling sound) may be annoying, but it's also life-affirming, helping the visually impaired, or the merely distracted, navigate a busy intersection.
Now a Petaluma, California artist-technologist has decided to up the street-corner affirmation quotient by redesigning a "crosswalk station" (the technical name for the button and its box, plus sign) to play positive messages contributed by people across America.
According to an article in the Petaluma Argus-Courier, Tim Dye was initially moved to set up the Push to Change World project by reading that the recorded directions in many of New York's crosswalk stations no longer play. Crossing a Petaluma street after pushing a button, Dye, 53, began to wonder what else a crosswalk station could do. He found one for sale on eBay and reprogrammed it. Then he began asking people he met on his cross-country travels to dictate a short, inspiring message, which he recorded and fed into the station's system.
He was careful to be open to all points of view; one contributor, for example, offered "Vote Trump to change the world."
"Other people said things like 'Remember that you can't take anything with you when you die,'" Dye tells the Argus-Courier, "or to just 'Ride bikes more and drive less.' It's whatever speaks to an individual."
With about 20 messages recorded (and edited to remove profanity and background sounds), he then attached the retooled button-and-box to several lampposts in downtown Petaluma, along with a sign: "Push to Change the World." He hung around the intersections to observe people's reactions, and often entered into conversations with them.
He's set up a phone number for additional contributions, and says that he would like to expand his project within Petaluma by collaborating with city organizations to place buttons elsewhere. He also envisages approaching the city to look at combining his upbeat messages with the directions in official crosswalk stations.
"What if it came on and said 'OK to cross Petaluma Boulevard, have a great day' or something like that," he asks in the article.
The stations could also tell secrets about the city, play restaurant recommendations from locals, or offer compliments, he suggests. "We live in a day and age where it's complete information pollution," he says. "I want to have objects that provide unique and interesting information when you need it."
Written by Public Art Review staff.
[Featured as a web-only piece, "Wait/Walk/Wisdom" during print publication of] Public Art Review #55.

redpajama_set_name: RedPajamaCommonCrawl


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Easily configure using browser-based configuration utility, or customize with Linux-based Open Source capabilities.
**While Linksys fully embraces the open source community and is providing open source use capabilities, they do not offer technical support on using open source firmware. Installing 3rd party firmware is done at your own risk and replacing factory-installed firmware with OpenWRT firmware will void your warranty. Please always seek the advice of more experienced users via open source community forums if you're unsure.


Success will always come hand in hand in life when you have a positive personality. But, a new study has shown idealistic results proving the fact that optimism can take you a long way beyond success in making you less prone to develop Type-2 diabetes.
Hence, low optimism, high negativity and hostility were associated with increased risk of incident diabetes in postmenopausal women, independent of major health behaviors and depressive symptoms, the study concluded.
"In addition to using personality traits to help us identify women at higher risk for developing diabetes, more individualized education and treatment strategies should also be used," said Joann Pinkerton, executive director at The North American Menopause Society.


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text:
US warns Beijing against force after Taiwan incursion by fighter jets
Taiwanese soldiers sit on a tank after an anti-invasion drill in January 2019. Taiwan scrambled aircraft following an incursion by Chinese jets on March 31.PHOTO: REUTERS
Apr 3, 2019, 7:21 am SGT
http://str.sg/ozDU
WASHINGTON (AFP) - The United States on Tuesday (April 2) warned Beijing against the use of "force or coercion" on Taiwan after the self-ruling island said that two Chinese fighter jets crossed a traditionally respected maritime line dividing the two sides.
"The United States opposes unilateral actions by any party that are aimed at altering the status quo, including anything related to force or coercion," State Department spokesman Robert Palladino told reporters.
"Beijing should stop its coercive efforts and resume dialogue with the democratically elected administration" in Taipei, he said.
Beijing - which considers Taiwan part of its territory awaiting reunification - has stepped up its jet and warship crossings near the island since the 2016 election of Beijing-sceptic President Tsai Ing-wen.
But going a step further, Taiwan's defence ministry said that two Chinese J-11 fighter jets took the highly unusual step on Sunday of crossing the median line in the Taiwan Strait that divides the mainland from the island.
Taiwan scrambled its own aircraft and protested against the "intentional, reckless and provocative action".
The US, like the vast majority of countries, recognises only Beijing, but it maintains a close relationship with Taiwan.
Taiwan condemns China after jets fly past maritime line
US wary of risk to Taiwan as China's military might grows
Under the 1979 Taiwan Relations Act passed by the US Congress, Washington is legally obliged to provide the island with the means to defend itself.
National security adviser John Bolton stressed US commitment for the Taiwan Relations Act in a tweet on Monday, amid events to mark the law's 40th anniversary.
"Chinese military provocations won't win any hearts or minds in Taiwan, but they will strengthen the resolve of people everywhere who value democracy. The Taiwan Relations Act and our commitment are clear," he wrote.


text:
Images of Doctors and their Implements: A Visual Dialogue between the Patient and the Doctor
Baker, Patricia A (2015) Images of Doctors and their Implements: A Visual Dialogue between the Patient and the Doctor. In: Petridou, Georgia and Kolleg, Max-Weber, eds. Homo Patiens - Approaches to the Patient in the Ancient World. Studies in Ancient Medicine (45). Brill, Leiden, pp. 365-389. ISBN 978-90-04-30555-7. (doi:10.1163/9789004305564_016) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
http://doi.org/10.1163/9789004305564_016
Images of physicians, patients, and medical instruments were placed on Graeco-Roman funerary monuments, altars and fresco paintings. These representations are examined here to determine whether there existed a standard convention by which physicians were depicted in order that the lay and possibly illiterate viewers could identify what the scene represented. Greek physicians were frequently shown with cupping vessels, midwives were seen with birthing stools, while Roman physicians were often shown with various surgical implements. It is argued that the correlation between the types of objects depicted with the medical practitioner was deliberately made by the artist to signify the nature of medicine in the individual practiced, to that the viewer could identify the role the practitioner had in their society
DOI/Identification number:
10.1163/9789004305564_016
Ancient Science & Medicine, Greek & Latin Literature, Classical Studies
C Auxiliary Sciences of History > CC Archaeology
Faculties > Humanities > School of European Culture and Languages
Jacqui Martlew
15 Dec 2015 15:29 UTC
Baker, Patricia A:
https://orcid.org/http//:orcid.org/0000-0002-6903-3834


text:
San Quentin News
Written By Incarcerated - Advancing Social Justice
Espanol Home
Wall City
'Get On The Bus' Offers San Quentin Inmates the Chance to Visit Loved Ones
July 1, 2015 by Juan Haines
For Brain Asey, doing time at San Quentin State Prison means being far away from his son and daughter who are living in Southern California.
"It's hard to be a parent behind bars because I'm not there when they need me," he said. "It's frustrating. All I can do is call or write letters."
Asey's son, nephew and mother took advantage of Get on the Bus (GOTB), a nonprofit organization that coordinates with the California Department of Corrections and Rehabilitation to bring children to incarcerated parents on Mother's Day and Father's Day.
This was the fourth year in a row Asey has benefited from the GOTB program.
"I missed seeing my daughter this time," Asey said. "They keep me strong in here. So, I look forward to the visits."
More than half of prisoners who are parents are incarcerated more than 100 miles from their children, and 10 percent live more than 500 miles away, according to the U.S. Department of Justice, Bureau of Justice Statistics.
Maintaining good communications with children and incarcerated parents has even gotten the attention of the children's television show, Sesame Street.
Tips for Incarcerated Parents, written and published by Sesame Street, gives advice on how to answer difficult questions a child may ask an incarcerated parent, as well as how to connect with their children during visits.
"It makes me want to support preserving
relationships between parents and kids"
The tips help prisoners deal with questions like: Where are you? When will you be home? Will I get to see you?
There are tips on helping the child feel comfortable during visits, on how to make the most of their visiting time, and how to make good-byes easier.
"Children are paying for a crime that they didn't commit," said Amalia Molina, executive director of Get on the Bus. "When the father goes to prison, it has a ripple effect on the child.
"It is very important to have children connect with their parents to show them that they are loved," said Molina, who works with the Center for Restorative Justice Works in Los Angeles.
Anna Hamilton, Cathy Kalin, Michelle Tapia, Dana Dart-McLean, Courtney Cayford and Antonio Luevano are GOTB volunteers who catered to the children and their guardians during the bus ride.
"I think it's really wonderful to see families connecting," said Tapia, a school counselor who works with children of incarcerated parents. "I see how challenging it is for the kids," she said. "It makes me want to support preserving relationships between parents and kids."
Darnell "Moe" Washington's daughter, Destiny Player, came to see him, along with his granddaughter, Khalieah Allen, his mother Bobbie Young, and sister Melinda Lockhart.
"I get to spend time with my daughter who's on college break," Washington said. "I only get to see them once a year and that's because of Get on the Bus program. It's a blessing and good program."
"We miss his presence in the family," his sister Melinda said. "He's the glue that keeps us together."
Washington's daughter, Destiny, attends college in New Orleans and majors in psychology.
"We have a good bond," she said. "I learn a lot about what he does in Restorative Justice."
Washington, who has been incarcerated for 18 years, said, "The biggest difference in me from the person I was, is that today is that I am able to forgive through the practices of Restorative Justice."
Visits from family and friends offer a means of establishing, maintaining, or enhancing social support networks, according to a study by Minnesota Department of Corrections Research Director, Grant Duwe.
The study finds that visitation can reduce recidivism by maintaining prisoners' social ties with family members, and by helping prisoners develop new bonds with clergy or mentors. In doing so, offenders can sustain or broaden their networks of social support.
Filed Under: Human Interest, Prison Programs
Made With Love At San Quentin State Prison


A rundown of account security and how to use authenticator without a phone. An update on RS mobile, summer weekends are on the way, and a bug to end all bugs on Old School RuneScape. Finally, a neutrino that left long ago from a galaxy far far away.


Beyond Fest is the highest attended genre film festival in the U.S. and exists to serve the genre community in Los Angeles.
Beyond Fest is built in partnership with American Cinematheque and Death Waltz Recording Co. Beyond Fest's mindbending designs courtesy of award-winning design studio La Boca.
A not-for-profit entity, Beyond Fest raises funds for the 501C3 non-profit film institution, American Cinematheque. Its favorite film is Jaws.
Established in 2002, La Boca is an award-winning independent design studio specializing in illustration and image-making. Since Beyond Fest's inception, La Boca has designed the festival's surreal artwork.


We now have confirmation that the Uomotos are safe. They were the last of the OPC personnel to be heard from.
Murray writes: "We are OK. Tremors continue. No water, utilities, internet yet. Thank you for your prayers."
Please continue in prayer for the people of Japan and especially for our sister churches there. Many difficult days are ahead.
Thanks to many who have called or sent e-mail to express your concern for us after the major earthquake on Friday, March 11. It was by far the worst we have experienced. We are all OK. When the earthquake hit, we had just assembled for our first Urayasu Church Plant planning meeting, which was soon transformed to an under-the-table prayer meeting. Hannah and Mary were at school a little more than an hour away. Relatively speaking, damage in our area was fairly minor—buckled streets and sidewalks, broken water pipes, fallen fences, lots of mud that has come up from underground. Other parts of the country have experienced much more terrible damage. I (Craig) just returned from standing in line for 2.5 hours to get a few containers of drinking water (we still have no running water). Ree is standing in a long line at the supermarket. Hannah and Mary have not yet been able to return from school (as of Saturday afternoon), but were able to stay with friends near the school. In God's providence, this terrible tragedy has provided opportunities for us to meet new people in our community and to take another step in relationships with new neighbors we have already met. Please pray that God would use even these circumstances to open Japanese hearts and to further His kingdom.
As we gather this coming Lord's Day to worship him, we again find that we have so much for which to be thankful. Please continue to pray for our brothers and sisters in Japan and for our missionaries who labor there to bring the good news of repentance and forgiveness of sin in Christ's name, that it might please our Lord to use the earthquake and the tsunami to open doors for us to show the compassion of Jesus and to proclaim the Word of life.


text:
package com.facebook.buck.rules;

import com.facebook.buck.model.Pair;
import com.facebook.buck.util.cache.FileHashCache;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.base.Function;
import com.google.common.base.Preconditions;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.ImmutableListMultimap;
import com.google.common.collect.ImmutableMap;
import com.google.common.collect.ImmutableSet;
import com.google.common.collect.Multimaps;
import com.google.common.hash.HashCode;
import com.google.common.hash.Hasher;
import com.google.common.hash.Hashing;

import java.io.DataInputStream;
import java.io.DataOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.file.NoSuchFileException;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Optional;

public class Manifest {

  private static final int VERSION = 0;

  private final RuleKey key;

  private final List<String> headers;
  private final Map<String, Integer> headerIndices;

  private final List<Pair<Integer, HashCode>> hashes;
  private final Map<HashCode, Integer> hashIndices;

  private final List<Pair<RuleKey, int[]>> entries;

  /**
   * Create an empty manifest.
   */
  public Manifest(RuleKey key) {
    this.key = key;
    headers = new ArrayList<>();
    headerIndices = new HashMap<>();
    hashes = new ArrayList<>();
    hashIndices = new HashMap<>();
    entries = new ArrayList<>();
  }

  /**
   * Deserialize an existing manifest from the given {@link InputStream}.
   */
  public Manifest(InputStream rawInput) throws IOException {
    DataInputStream input = new DataInputStream(rawInput);

    // Verify the manifest version.
    int version = input.readInt();
    Preconditions.checkState(
        version == VERSION,
        "invalid version: %s != %s",
        version,
        VERSION);

    key = new RuleKey(input.readUTF());

    int numberOfHeaders = input.readInt();
    headers = new ArrayList<>(numberOfHeaders);
    headerIndices = new HashMap<>(numberOfHeaders);
    for (int index = 0; index < numberOfHeaders; index++) {
      String header = input.readUTF();
      headers.add(header);
      headerIndices.put(header, index);
    }

    int numberOfHashes = input.readInt();
    hashes = new ArrayList<>(numberOfHashes);
    hashIndices = new HashMap<>(numberOfHashes);
    for (int index = 0; index < numberOfHashes; index++) {
      int headerIndex = input.readInt();
      HashCode headerHash = HashCode.fromString(input.readUTF());
      hashes.add(new Pair<>(headerIndex, headerHash));
      hashIndices.put(headerHash, index);
    }

    int numberOfEntries = input.readInt();
    entries = new ArrayList<>(numberOfEntries);
    for (int entryIndex = 0; entryIndex < numberOfEntries; entryIndex++) {
      int numberOfEntryHashes = input.readInt();
      int[] entryHashes = new int[numberOfEntryHashes];
      for (int hashIndex = 0; hashIndex < numberOfEntryHashes; hashIndex++) {
        entryHashes[hashIndex] = input.readInt();
      }
      RuleKey key = new RuleKey(input.readUTF());
      entries.add(new Pair<>(key, entryHashes));
    }
  }

  public RuleKey getKey() {
    return key;
  }

  private Integer addHash(String header, HashCode hash) {
    Integer headerIndex = headerIndices.get(header);
    if (headerIndex == null) {
      headers.add(header);
      headerIndex = headers.size() - 1;
      headerIndices.put(header, headerIndex);
    }

    Integer hashIndex = hashIndices.get(hash);
    if (hashIndex == null) {
      hashes.add(new Pair<>(headerIndex, hash));
      hashIndex = hashes.size() - 1;
      hashIndices.put(hash, hashIndex);
    }

    return hashIndex;
  }

  @VisibleForTesting
  protected static HashCode hashSourcePathGroup(
      FileHashCache fileHashCache,
      SourcePathResolver resolver,
      ImmutableList<SourcePath> paths)
      throws IOException {
    if (paths.size() == 1) {
      return hashSourcePath(paths.asList().get(0), fileHashCache, resolver);
    }
    Hasher hasher = Hashing.md5().newHasher();
    for (SourcePath path : paths) {
      hasher.putBytes(hashSourcePath(path, fileHashCache, resolver).asBytes());
    }
    return hasher.hash();
  }

  private static HashCode hashSourcePath(
      SourcePath path,
      FileHashCache fileHashCache,
      SourcePathResolver resolver) throws IOException {
    if (path instanceof ArchiveMemberSourcePath) {
      return fileHashCache.get(resolver.getAbsoluteArchiveMemberPath(path));
    } else {
      return fileHashCache.get(resolver.getAbsolutePath(path));
    }
  }

  private boolean hashesMatch(
      FileHashCache fileHashCache,
      SourcePathResolver resolver,
      ImmutableListMultimap<String, SourcePath> universe,
      int[] hashIndices)
      throws IOException {
    for (int hashIndex : hashIndices) {
      Pair<Integer, HashCode> hashEntry = hashes.get(hashIndex);
      String header = headers.get(hashEntry.getFirst());
      ImmutableList<SourcePath> candidates = universe.get(header);
      if (candidates.isEmpty()) {
        return false;
      }
      HashCode onDiskHeaderHash;
      try {
        onDiskHeaderHash = hashSourcePathGroup(fileHashCache, resolver, candidates);
      } catch (NoSuchFileException e) {
        return false;
      }
      HashCode headerHash = hashEntry.getSecond();
      if (!headerHash.equals(onDiskHeaderHash)) {
        return false;
      }
    }
    return true;
  }

  /**
   * @return the {@link RuleKey} of the entry that matches the on disk hashes provided by
   *     {@code fileHashCache}.
   */
  public Optional<RuleKey> lookup(
      FileHashCache fileHashCache,
      SourcePathResolver resolver,
      ImmutableSet<SourcePath> universe)
      throws IOException {
    ImmutableListMultimap<String, SourcePath> mappedUniverse =
        Multimaps.index(universe, sourcePathToManifestHeaderFunction(resolver));
    for (Pair<RuleKey, int[]> entry : entries) {
      if (hashesMatch(fileHashCache, resolver, mappedUniverse, entry.getSecond())) {
        return Optional.of(entry.getFirst());
      }
    }
    return Optional.empty();
  }

  private static Function<SourcePath, String> sourcePathToManifestHeaderFunction(
      final SourcePathResolver resolver) {
    return input -> sourcePathToManifestHeader(input, resolver);
  }

  private static String sourcePathToManifestHeader(
      SourcePath input,
      SourcePathResolver resolver) {
    if (input instanceof ArchiveMemberSourcePath) {
      return resolver.getRelativeArchiveMemberPath(input).toString();
    } else {
      return resolver.getRelativePath(input).toString();
    }
  }

  /**
   * Adds a new output file to the manifest.
   */
  public void addEntry(
      FileHashCache fileHashCache,
      RuleKey key,
      SourcePathResolver resolver,
      ImmutableSet<SourcePath> universe,
      ImmutableSet<SourcePath> inputs)
      throws IOException {
    int index = 0;
    int[] hashIndices = new int[inputs.size()];
    ImmutableListMultimap<String, SourcePath> sortedUniverse =
        Multimaps.index(
            universe,
            sourcePathToManifestHeaderFunction(resolver));
    for (SourcePath input : inputs) {
      String relativePath = sourcePathToManifestHeader(input, resolver);
      ImmutableList<SourcePath> paths = sortedUniverse.get(relativePath);
      Preconditions.checkState(!paths.isEmpty());
      hashIndices[index++] =
          addHash(
              relativePath,
              hashSourcePathGroup(fileHashCache, resolver, paths));
    }
    entries.add(new Pair<>(key, hashIndices));
  }

  /**
   * Serializes the manifest to the given {@link OutputStream}.
   */
  public void serialize(OutputStream rawOutput) throws IOException {
    DataOutputStream output = new DataOutputStream(rawOutput);

    output.writeInt(VERSION);

    output.writeUTF(key.toString());

    output.writeInt(headers.size());
    for (String header : headers) {
      output.writeUTF(header);
    }

    output.writeInt(hashes.size());
    for (Pair<Integer, HashCode> hash : hashes) {
      output.writeInt(hash.getFirst());
      output.writeUTF(hash.getSecond().toString());
    }

    output.writeInt(entries.size());
    for (Pair<RuleKey, int[]> entry : entries) {
      output.writeInt(entry.getSecond().length);
      for (int hashIndex : entry.getSecond()) {
        output.writeInt(hashIndex);
      }
      output.writeUTF(entry.getFirst().toString());
    }
  }

  public int size() {
    return entries.size();
  }

  @VisibleForTesting
  ImmutableMap<RuleKey, ImmutableMap<String, HashCode>> toMap() {
    ImmutableMap.Builder<RuleKey, ImmutableMap<String, HashCode>> builder = ImmutableMap.builder();
    for (Pair<RuleKey, int[]> entry : entries) {
      ImmutableMap.Builder<String, HashCode> entryBuilder = ImmutableMap.builder();
      for (int hashIndex : entry.getSecond()) {
        Pair<Integer, HashCode> hashEntry = hashes.get(hashIndex);
        String header = headers.get(hashEntry.getFirst());
        HashCode headerHash = hashEntry.getSecond();
        entryBuilder.put(header, headerHash);
      }
      builder.put(entry.getFirst(), entryBuilder.build());
    }
    return builder.build();
  }

  @VisibleForTesting
  static Manifest fromMap(RuleKey key, ImmutableMap<RuleKey, ImmutableMap<String, HashCode>> map) {
    Manifest manifest = new Manifest(key);
    for (Map.Entry<RuleKey, ImmutableMap<String, HashCode>> entry : map.entrySet()) {
      int entryHashIndex = 0;
      int[] entryHashIndices = new int[entry.getValue().size()];
      for (Map.Entry<String, HashCode> innerEntry : entry.getValue().entrySet()) {
        entryHashIndices[entryHashIndex++] =
            manifest.addHash(innerEntry.getKey(), innerEntry.getValue());
      }
      manifest.entries.add(new Pair<>(entry.getKey(), entryHashIndices));
    }
    return manifest;
  }

}

redpajama_set_name: RedPajamaGithub


text:
Former French president Nicolas Sarkozy to face corruption and influence peddling charges
Posted Mon 23 Nov 2020 at 8:27am Monday 23 Nov 2020 at 8:27am Mon 23 Nov 2020 at 8:27am
Nicolas Sarkozy will stand trial in Paris on corruption charges. (AP: Valery Hache)
abc.net.au/news/former-france-president-nicolas-sarkozy-faces-corruption-charges/12912512
Former French president Nicolas Sarkozy is set to go on trial on charges of corruption and influence peddling in a phone-tapping scandal, a first for the 65-year-old politician who has faced several other judicial investigations since leaving office in 2012.
Nicolas Sarkozy faces up to 10 years in prison if found guilty of corruption and influence peddling
Mr Sarkozy denies any wrongdoing and says he is in a "combative" mood ahead of the trial
This is the first time a former president has faced trial for corruption in France
Mr Sarkozy is accused of trying to illegally obtain information from a magistrate about an investigation involving him in 2014.
He will stand trial in a Paris court along with his lawyer, Thierry Herzog, 65, and the magistrate, Gilbert Azibert, 73.
They face up to 10 years' prison and a maximum fine of 1 million euros ($1.6 million).
They deny any wrongdoing.
Mr Sarkozy and Mr Herzog are suspected of promising Mr Azibert a job in Monaco in exchange for leaking information about an investigation into suspected illegal financing of the 2007 presidential campaign by France's richest woman, L'Oreal heiress Liliane Bettencourt.
In 2014, Mr Sarkozy and Mr Herzog used secret mobile phones — registered to the alias name of "Paul Bismuth" — to have private talks because they feared their conversations were being tapped.
Mr Sarkozy and Mr Herzog explained they bought the phones to avoid being targeted by illegal phone tapping. Investigative judges, however, suspect they actually wanted to avoid being tapped by investigators.
Judges have found that discussions between Mr Sarkozy and his lawyer suggested they had knowledge judicial investigators at the time tapped their conversations on their official phones, as they mentioned "judges listening".
Thierry Herzog speaks with Nicolas Sarkozy's son Pierre at a football match in 2017. (Reuters: Charles Platiau)
Mr Sarkozy has argued he did not intervene to help Mr Azibert, who never got the job and retired in 2014.
Investigative judges consider that as soon as a deal has been offered, it constitutes a criminal offence even if the promises have not been fulfilled.
Legal proceedings against Mr Sarkozy have been dropped in the Bettencourt case.
Mr Sarkozy pointed at judicial harassment, accusing judges of breaching lawyer-client privilege via wiretapping.
"I don't want things that I didn't do to be held against me. The French need to know … that I'm not a rotten person," he told news broadcaster BFM earlier this month.
He said he was facing the trial in a "combative" mood.
Former French president Nicolas Sarkozy is facing up to 10 years in prison. (Reuters: Eric Feferberg/Pool)
This is the first time a former president has faced trial for corruption in France.
Mr Sarkozy's predecessor, Jacques Chirac, was found guilty in 2011 of misuse of public money, breach of trust and conflict of interest and given a two-year suspended prison sentence for actions during his time as Paris mayor, before he was president from 1995 to 2007.
Mr Sarkozy's name has appeared for years in several other judicial investigations.
Allegations, which include illegal financing of his 2007 campaign by then-Libyan dictator Moammar Gadhafi, cast a shadow over Mr Sarkozy's comeback attempt for the 2017 presidential election.
After failing to be chosen as candidate by his conservative party, he withdrew from active politics.
Mr Sarkozy remained the most popular figure amid French right-wing voters in recent years. His memoirs published this year, The Time of Storms, was a bestseller for weeks.
Posted 23 Nov 2020 23 Nov 2020 Mon 23 Nov 2020 at 8:27am
Jean Castex named as France's new Prime Minister
Novak Djokovic claims 10th Australian Open title and record-equalling 22nd men's singles grand slam
live: Novak Djokovic claims 10th Australian Open title and record-equalling 22nd men's singles grand slam


text:
Whitted and Houston together again with Westchester Knicks
Allan Houston is the GM and Kevin Whitted is the new coach of the NBA D-League expansion team. They are former teammates at Tennessee.
Whitted and Houston together again with Westchester Knicks Allan Houston is the GM and Kevin Whitted is the new coach of the NBA D-League expansion team. They are former teammates at Tennessee. Check out this story on lohud.com: http://lohud.us/1xvPL5U
Brian Heyman, bheyman@lohud.com Published 10:05 p.m. ET Oct. 9, 2014 | Updated 10:23 p.m. ET Oct. 9, 2014
Westchester Knicks General Manager Allan Houston, left, was at Children's Village in Dobbs Ferry to introduce the team's new head coach, Kevin Whitted Oct. 9, 2014.(Photo: Peter Carr/The Journal News)Buy Photo
Kevin Whitted is the first head coach of the Westchester Knicks. The 43-year-old North Carolina native has a history with player development.
DOBBS FERRY – Kevin Whitted kept in touch with Allan Houston, two ex-basketball players now in their early 40s who can take a trip back in time together to when they were Tennessee teammates.
"He liked to imitate people, so you know he's paying attention to details," Houston said. "But I'm really more impressed and proud of his path afterward, his work ethic and his humility."
Houston went on to become a shooting star in the backcourt and an executive with the Knicks. Whitted's path took him mostly to Europe to play professionally, then to the minor leagues for eight years of coaching. And he opened a business in player development, which is a passion for him. He told Houston if anything ever came up, he was ready and available.
Something came up. And there they were Thursday on the gym floor at Children's Village, striking happy poses for the cameras, doing interviews and helping run a clinic for the students.
Houston is the GM of the NBA Development League's Westchester Knicks, the expansion team that will serve as the affiliate of the MSG tenant. And Whitted has been hired as the first head coach. This was the official introduction.
"This is a great opportunity for myself, a great opportunity for my family as well," Whitted said. "We're very excited about this. I'm just looking forward to getting started."
Roster-building will seriously start with a draft Nov. 1. Training camp opens three days later. The season tips off Nov. 16 at Oklahoma City, and the home schedule begins three days later against Canton at the County Center.
While new Knicks coach Derek Fisher is installing the triangle offense, the preferred system of the organization's new boss, Phil Jackson, Whitted is about to become Big Chief Triangle of the D-League, installing the same system.
"I'm well versed," Whitted said. "I used it a lot with my other minor-league teams that I coached previously before I was an assistant in the D-League. I ran it as a player as well under Jim Cleamons when he coached with the Mavericks. So that's where it was introduced to me (in a tryout), and I basically embraced it from that point on."
Whitted is from Wilmington, N.C. He broke Michael Jordan's all-time scoring record at Laney High. How about that for credibility?
"Michael gives me a hard time about it when I run into him," Whitted said. "He basically tells me, 'Well, the gym was named after me, so that means more.' We have a nice competitive conversation about it, but it's all in fun."
Houston said the 43-year-old former forward is under no pressure to win. But when asked how he views his job, in terms of wins and losses or player development, Whitted said, "It's all of the above. I think player development is essential. That's something we have to focus on immediately. This gives me a chance to sharpen my coaching skills as well."
While the players in the D-League want to move up to the NBA one day, Whitted, in a sense, is no different.
"I think everyone wants to get there," Whitted said. "I'm not in any rush at this point. Right now, I'm just trying to develop as a coach and as a developer and other areas as well. I think at this level you have to touch everything, which gives you grass roots to every part of the business."
Twitter: @bheyman99
Westchester Knicks coach Kevin Whitted introduced
Westchester Knicks new head coach Kevin Whitted is introduced at Children's Village in Dobbs Ferry Oct. 9, 2014. Peter Carr/The Journal News
Westchester Knicks General Manager Allan Houston, left, was at Children's Village in Dobbs Ferry to introduce the team's new head coach, Kevin Whitted Oct. 9, 2014. Peter Carr/The Journal News
Westchester Knicks General Manager Allan Houston, left, and new head coach, Kevin Whitted pose with residents of Children's Village in Dobbs Ferry Oct. 9, 2014. Peter Carr/The Journal News
Westchester Knicks General Manager Allan Houston was at Children's Village in Dobbs Ferry to introduce the Westchester Knicks new head coach, Kevin Whitted Oct. 9, 2014. Peter Carr/The Journal News
NY Rangers' Brendan Lemieux close to returning
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News -Acrylic Display, Acrylic Display Box, Acrylic Stand Holder, Factory China, Manufacturer, Exporter -Shenzhen Yida Acrylic Product Manufacture Co,. Ltd.
Do you know how to make a acrylic display case? We think you can solve this problem by making a custom case in the best way possible.
Acrylic display is widely used in electronics, electrical appliances, famous tobacco, wine, pharmacy, glasses, craft gifts, crystal products, hotel supplies, stationery, automotive supplies, 4S stores Model cars, plastics, cosmetics store, factory product showrooms and foreign trade companies samples. Acylis dispaly can also be used for business fairs and can be designed for more styles to make products highlights.
In recently years, the acrylic display widely used in the POS industry, more and more pos designer prefer to use this material to custom the display and increase the sales.
This is for Acrylic Display Case/Boxes Introduction, acrylic case is a cabinet made by acrylic material,usually used to display the product for watching, for example in a store, museum, restaurant or convention etc.
Acrylic frame is made by a kind of acrylic material, it is a good way of displaying your photos and art design, it is very popular in public.
There are numbers of key benefits that make acrylic display tools top sought especially to the retailer segment. Despite the fact that acrylic glass does not appear very sturdy, but in practicality they can withstand a lot of weight and pressure. Hence, as it comes to durability factor, one of its unique features is also longevity. The transparency is a vital factor as it matters to display units. The acrylic display offers unique clearness enabling the customers to view the products, brochures or campaigning literatures easily. In addition, acrylic is quite lighter than any other display materials like glass, metals or woods.
The stands are designed out of varieties of materials including wood, metal and glass apart from acrylic poly glass. Acrylic display units are made from these glass items and due to numbers of advantages, the display stands are widely recognized by retail outlets, sales counters and other places across the world.
The retailing hubs are simply restless to spread innovative promotional tools and messages to attract enhanced consumers. Among varieties of promotional as well display tools, acrylic display items are in great demand now for its state-of-the-art design, cost effectiveness and versatility.
The acrylic display is a new generation concept and exhibiting tool, which can hold an extensive array of products ranging from food items to footwear. Whether you are a owner of a huge department store or a small shop and deal in watches, toys or domestic items, you can make great use of this versatile displayers. If we consider the modern retail sales business and industry, unsurprisingly its product sales as well marketing depend greatly upon the mechanism of displays used.
China is a hub for manufacturing corporate gifting accessories at economical price. The place has an exclusive assortment of gifting accessories and acrylic display items which is in high demand all over the world. These products are used in high-end corporate societies and even promotional events.
Copyright © 2003 Shenzhen Yida Acrylic Product Manufacture Co,. Ltd. All Rights Reserved. Designed by Agewnet.com.


Unisagaz Plunk O Matic Crush The Castle 2 Supermarket Tom and Jerry Room..
Description: Jump from one leaf to another and don't fall to the river. If you do then the game is over. Try to get as far as possible. To receive more points try to hit dragonflies flying above. Use mouse to set the angle and then press left button to set the power of jump.


text:
Q: What is the difference between a vortex ring and a circular line vortex? Can someone explain the difference between a vortex ring and a circular line vortex? Or are they the same?

A: A vortex ring has a finite core radius $a$. The circular line vortex is a vortex ring with an infinitesimal core radius $a\to 0$. It is unphysical and only occurs in an inviscid fluid.

redpajama_set_name: RedPajamaStackExchange


text:
Marines to discharge sergeant who criticized Obama online
Published: APRIL 25, 2012 23:19
LOS ANGELES - A US Marine sergeant who wrote in a Facebook post that he would not follow orders from President Barack Obama will be discharged from the military on "other than honorable" terms, a Marine spokesman said on Wednesday.
California-based Sergeant Gary Stein was advised of the decision after a commanding general upheld the recommendation by a review board, Major Michael Armistead said.
"He was formally informed of that today, of the separating authority's decision. Now he will go through the transition (process) required to leave the Marines," Armistead said. That transition can take up to 20 days, he said.


text:
Thalaivar Frenzy - an Ode to Rajnikanth
By sahanasehgal
Kabali's release was one of the most auspicious and celebrated days in Tamil Nadu.
Rajnikanth's block buster, Kabali's release seemed like a grand fest. In fact, it triumphed all the festivals of the year. If you are in Tamil Nadu during a Rajnikanth movie release, you're in for an absolute treat. It is the best time to work in a cinema theatre; that's the only sure shot way of getting a ticket to the film. If you decide to buy fifteen tickets and sell them outside the theatre during the first weekend, you could name any insane price you want and people would pay up!
Fans have been up since 4 a.m., gearing up for the 8:10 a.m. show, the first show of the day. Any hardcore Thalaivar fan worth their salt will not miss the first day, first show. The streets resemble nothing short of a parade. 15 feet cardboard cutouts of the superstar in all his glory are erected in street corners with a DJ roaring and fans dancing in front of their One True God. Being held up in traffic for the better part of an hour made me realise that this was no ordinary affair. Every Friday, films are being released across the country. They come and go, nobody cares. And yet, here were fans that performed a milk abhishekam and puja in front of Rajnikanth cutouts so the film would be successful.
As this was my first time experiencing the Thalaivar frenzy, I was naive enough to call BookMyShow to try to get a ticket. The harried girl who answered my call thought I had gone crazy to think I could get a ticket on the first day without booking in advance.
I did watch the movie though, on a Monday, no less. I had to see what all the drama was about; I was not disappointed. The ground nearly shook as the crowd screamed when the music came on and in blue block letter the words 'SUPERSTAR RAJNI' lit the screen. In a cliched cinematographic move, they did not show the Thalaivar's face clearly at first. This was the very face plastered on every wall across Trichy, but the euphoric fans screamed like they'd seen it for the first time. In their defense, you have to agree, Rajnikanth's got serious swag, with the cool blue tinted glasses and a highly classy wardrobe. During the fight scenes, I would worry that Kabali was alone and did not seem to have a gun on him but this sleek rod or gun would slide out of his sleeve and my doubts would be assuaged.
Being half Tamilian and mostly raised in Mumbai, I did not understand many keywords and annoyed the man sitting next to me. When Kabali got shot and the screen went black for the intermission, I turned in panic to the man beside me who had to calm me down. Being a veteran Rajnikant fan, he very confidently said, "He'll be back." I thought I was above all this devotion, not really, I guess. From Baasha in 1995 to Kabali in 2016; from dialogues like 'Na oru darva sonna nooru darva sonna maari' to 'Ye vazhi tani vazhi' to something as simple as 'Kabalidda', it's been Rajnikanth, all the way!
Nobody was above the craze.
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