text:
\section{Introduction}

The standard Heisenberg uncertainty principle (HUP) \cite{1} of quantum
mechanics represents one of the fundamental properties of quantum systems.
According to HUP, there should be a fundamental limit for the measurement
accuracy where certain pairs of physical observables, such as the positions
and momenta or energy and time, cannot be simultaneously measured with full
accuracy. A large number of studies have converged on the idea that the HUP
should be reformulated for systems with energies close to the Planck scale
\kappa $, which incorporates the concept of minimum measurable length \cit
{2,3,4,5,6}. The minimum measurable length idea is predicted by different
tentative approaches to quantum gravity such as string theory \cite{7,8},
quantum geometry \cite{9,10}, loop quantum gravity \cite{11} and black hole
physics \cite{12,13}. This fundamental scale leads to a modification of the
Heisenberg uncertainty principle to the so-called generalized uncertainty
principle (GUP) \cite{14,15,16}. The GUP ideas are characterized by a
deformation of the classical Heisenberg uncertainty relation and the most
widely adopted generalization of the Heisenberg uncertainty principle reads
\cite{14},
\begin{equation}
\left( \Delta X\right) \left( \Delta P\right) \geqslant \frac{\hbar }{2
\left( 1+l_{p}\left( \Delta P\right) ^{2}\right) .
\end{equation}
If $l_{p}$ is a positive constant, the formula implies the existence of a
minimal momentum uncertainty. If $l_{p}$ is a negative constant, no minimal
uncertainty occurs.

On the other hand, there exists another form of the deformed Heisenberg
uncertainty principle which is called the extended uncertainty principle
(EUP) \cite{17,18,19,20,21,22} which takes into account the large distances
where, due to gravity, the spacetime is curved. We have,
\begin{equation}
\left( \Delta X_{i}\right) \left( \Delta P_{i}\right) \geqslant \frac{\hbar
}{2}\left( 1+\frac{\left( \Delta X_{i}\right) ^{2}}{l_{H}^{2}}\right) ,
\end{equation
where $l_{H}$ is the (anti-)de Sitter radius which is related to the
cosmological constant ($\Lambda $) as $\Lambda =-3/l_{H}^{2}$. The
EUP modifies the standard commutation relations between position and, the
momentum and the coordinate representation of the momentum operators for
this model become position-dependent.

S. Mignemi showed that EUP can be derived from the geometric properties of
the (anti-)de Sitter spacetime, with a suitable parametrization \cite{17}.
In addition to this, it is shown that the EUP arises naturally from the
first terms in the expansion of any metric, which means that the corrections
to the Hawking temperature of Schwarzschild black hole can be computed by
incorporating the gravitational interaction as an external force on a flat
background, and neglecting the curvature of spacetime \cite{18}. To our
knowledge, only a few works have studied the influence of extended
uncertainty principle on quantum mechanical problems \cit
{23,24,25,26,27,28,29,30,31,32,33,34,35}.

In this paper, we study the problem of relativistic Coulomb potential in the
framework of the extended uncertainty principle in (3+1) dimensional
spacetimes. We solve the problem of Coulomb potential for the Klein-Gordon
and Dirac equations to get the exact form of the energy levels and
eigenfunctions. This paper is organized as follows: In Sect. 2, we introduce
the main relations of quantum mechanics with the extended uncertainty
principle. In sections 3 and 4, we solve the Klein-Gordon and Dirac
equations exactly in (3+1) dimensions with the Coulomb-like interaction in
the context of EUP in the position space representation. Section 5 contains
the conclusion.

\section{The Extended Uncertainty Relation}

In three-dimensional space, the modified Heisenberg algebra leading to EUP
is given by the following deformed commutation relations \cite{17},
\begin{eqnarray}
\left[ X_{i},P_{j}\right]  &=&i\hslash \left( \delta _{ij}-s\lambda
X_{i}X_{j}\right) ;\text{ }i=j=1,2,3,  \notag \\
\left[ X_{i},X_{j}\right]  &=&0;\text{ \  \ }\left[ P_{i},P_{j}\right]
=-i\hslash s\lambda L_{ij},  \label{3}
\end{eqnarray
where $\lambda =-\frac{1}{l_{H}^{2}s}$ is a small parameter of dimension of
inverse distance squared, $L_{ij}=X_{i}P_{j}-X_{j}P_{i}$, $s=1$ for de
Sitter space and $s=-1$ for anti-de Sitter space. These commutation
relations lead to the extended uncertainty principle,
\begin{equation}
\left( \Delta X_{i}\right) \left( \Delta P_{i}\right) \geq \frac{\hslash }{2
\left( 1-s\lambda \left( \Delta X_{i}\right) ^{2}\right) .  \label{4}
\end{equation
In anti-de Sitter space $\left( s=-1\right) ,$ the uncertainty relation (\re
{4}) is characterized by the appearance of a non-zero minimal uncertainty in
momentum (MUM),
\begin{equation}
\left( \Delta P_{k}\right) _{\min }=\frac{\hslash \sqrt{\lambda }}{2},\text{
\  \  \ }\forall k,
\end{equation
and for the case of de Sitter space $\left( s=1\right) $, no lower bound on
the measurable length arises. An explicit representation of the momentum and
position operators obeying Eq. (\ref{3}) is given by,
\begin{eqnarray}
X_{i} &=&\frac{x_{i}}{\sqrt{1+s\lambda r^{2}}},\text{ \  \  \ where
r=\sum_{i=1}^{3}x_{i}^{2}\text{.} \\
P_{i} &=&\frac{\hslash }{i}\sqrt{1+s\lambda r^{2}}\frac{\partial }{\partial
x_{i}},
\end{eqnarray
in the position representation. In (anti-)de sitter space, the scalar
product is not the usual one, but it is defined as,
\begin{equation}
\left \langle \phi \right. \left \vert \psi \right \rangle =\int \frac{d\vec{r
}{\sqrt{1+s\lambda r^{2}}}\phi ^{\dagger }\left( \vec{r}\right) \psi \left(
\vec{r}\right) ,
\end{equation
which preserves the hermiticity of the position operator.

\section{Klein-Gordon Equation for the Hydrogen Atom}

In this section, we will study the eigenvalue problem of the Klein-Gordon
equation for a Coulomb-type interaction in (3+1) dimensional spacetime. We
have,
\begin{equation}
\left[ \left( E+\frac{Ze^{2}}{R}\right) ^{2}-c^{2}P^{2}-m^{2}c^{4}\right]
\psi =0.  \label{9}
\end{equation}
In de Sitter space, the momentum squared and distance operators act in
coordinate space a
\begin{equation}
P^{2}\psi =-\hbar ^{2}\left[ \left( 1+\lambda r^{2}\right) \left( \frac
\partial ^{2}}{\partial r^{2}}+\frac{2}{r}\frac{\partial }{\partial r}-\frac
\hat{L}^{2}}{\hslash ^{2}r^{2}}\right) +\lambda r\frac{\partial }{\partial r
\right] \psi ,  \label{10}
\end{equation
\begin{equation}
R\psi =\frac{r}{\sqrt{1+\lambda r^{2}}}\psi ,  \label{11}
\end{equation}
where $\hat{L}$ is the orbital angular momentum operator whose
eigenfunctions are given in terms of the spherical harmonics
\begin{equation}
\hat{L}^{2}Y_{\ell ,\nu }\left( \theta ,\varphi \right) =\hslash ^{2}\ell
\left( \ell +1\right) Y_{\ell ,\nu }\left( \theta ,\varphi \right) ,
\end{equation}
where $\ell$ and $\nu$ are quantum numbers. Using (\ref{10}) and (\ref{11})
in Eq. (\ref{9}), we obtain
\begin{equation}
\left[ \left( 1+\lambda r^{2}\right) \left( \frac{\partial ^{2}}{\partial
r^{2}}+\frac{2}{r}\frac{\partial }{\partial r}-\frac{\hat{L}^{2}}{\hslash
^{2}r^{2}}\right) +\lambda r\frac{\partial }{\partial r}+\frac{2Z\mu E}
\hbar c}\frac{\sqrt{1+\lambda r^{2}}}{r}+\left( Z\mu \right) ^{2}\frac
\left( 1+\lambda r^{2}\right) }{r^{2}}+\frac{E^{2}-m^{2}c^{4}}{\hbar
^{2}c^{2}}\right] \psi =0,
\end{equation
where $\mu =\frac{e^{2}}{\hbar c}\simeq 1/137.03602$ is Sommerfeld's
fine-structure constant and $\frac{2\pi \hbar }{m}=2.4263\times 10^{-12}$m
is the Compton wavelength. For the wave function $\psi$, we make the ansatz,
\begin{equation}
\psi =\frac{\digamma _{\ell }\left( r\right) }{\sqrt{r}}Y_{\ell ,\nu }\left(
\theta ,\varphi \right).
\end{equation}
The angular and radial dependent parts can now be separated to yield the
radial equation
\begin{equation}
\left[ \left( 1+\lambda r^{2}\right) \left( \frac{d^{2}}{dr^{2}}+\frac{1}{r
\frac{d}{dr}-\frac{\delta ^{2}}{r^{2}}\right) +\lambda r\frac{d}{dr}+\frac
2Z\mu E}{\hbar c}\frac{\sqrt{1+\lambda r^{2}}}{r}+\frac{E^{2}-m^{2}c^{4}}
\hbar ^{2}c^{2}}-\frac{\lambda }{2}\right] \digamma _{\ell }\left( r\right)
=0,  \label{15}
\end{equation
with $\delta ^{2}=\left( \ell +\frac{1}{2}\right) ^{2}-\left( Z\mu \right)
^{2}.$ Let us now transform Eq. (\ref{15}) into a hypergeometric
differential equation by using two successive changes of variables as
\begin{equation}
\varkappa =\frac{\sqrt{1+\lambda r^{2}}}{\sqrt{\lambda }r}\text{ and }y
\frac{1}{2}\left( 1-\varkappa \right) .
\end{equation
Equation (\ref{15}) takes the form,
\begin{equation}
\left[ y\left( 1-y\right) \frac{\partial ^{2}}{\partial y^{2}}+\left( \frac{
}{2}-y\right) \frac{\partial }{\partial \varkappa }-\frac{\delta ^{2}-\frac
2Z\mu E}{\hbar c\sqrt{\lambda }}-\frac{E^{2}-m^{2}c^{4}}{\hbar
^{2}c^{2}\lambda }-\frac{1}{2}}{4y}-\frac{\delta ^{2}+\frac{2Z\mu E}{\hbar
\sqrt{\lambda }}-\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}\lambda }-\frac{1}{2
}{4\left( 1-y\right) }+\delta ^{2}\right] \digamma _{\ell }\left( y\right)
=0.  \label{17}
\end{equation
The latter equation possesses three regular singular points located at
y=\{0,1,\infty \}$. Applying the definition
\begin{equation}
\digamma _{\ell }\left( y\right) =y^{a}\left( 1-y\right) ^{b}\Xi _{\ell
}\left( y\right),
\end{equation
the Eq. (\ref{17}) will reduce to the hypergeometric type, namely,
\begin{equation}
\left \{ y\left( 1-y\right) \frac{\partial ^{2}}{\partial y^{2}}+\left(
\frac{1}{2}+2a-y\left( 1+2a+2b\right) \right) \frac{\partial }{\partial y}
\left[ \left( a+b\right) ^{2}-\delta ^{2}\right] \right \} \Xi _{\ell
}\left( y\right) =0,  \label{19}
\end{equation}
where $a$ and $b$ are given b
\begin{eqnarray}
a &=&\frac{1}{4}+\frac{1}{2}\sqrt{\delta ^{2}-\frac{2Z\mu E}{\hbar c\sqrt
\lambda }}-\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}\lambda }+\frac{3}{4}}, \\
b &=&\frac{1}{4}+\frac{1}{2}\sqrt{\delta ^{2}+\frac{2Z\mu E}{\hbar c\sqrt
\lambda }}-\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}\lambda }+\frac{3}{4}}.
\end{eqnarray
The regular solution at the origin $y=0$ of Eq.(\ref{19}) is written in
terms of the hypergeometric function as
\begin{equation}
\Xi _{\ell }\left( y\right) =\mathbf{F}\left( A;B;\frac{1}{2}+2a;y\right) ,
\end{equation}
whose parameters are given b
\begin{equation}
A=a+b-\delta ;\text{ \ }B=a+b+\delta .
\end{equation}
The hypergeometric function becomes a polynomial of degree $n$ whe
\begin{equation}
A=-n\text{ \  \ or \ }B=-n\text{ \  \ where }n=0,1,2,...
\end{equation
In both cases, we have
\begin{equation}
\frac{1}{2}+\frac{1}{2}\sqrt{\delta ^{2}+\frac{3}{4}+\frac{m^{2}c^{4}}{\hbar
^{2}c^{2}\lambda }-\frac{2Z\mu E}{\hbar c\sqrt{\lambda }}-\frac{E^{2}}{\hbar
^{2}c^{2}\lambda }}+\frac{1}{2}\sqrt{\delta ^{2}+\frac{3}{4}+\frac{m^{2}c^{4
}{\hbar ^{2}c^{2}\lambda }+\frac{2Z\mu E}{\hbar c\sqrt{\alpha }}-\frac{E^{2
}{\hbar ^{2}c^{2}\lambda }}+\delta =-n.  \label{25}
\end{equation}
The energy spectrum can be obtained from (\ref{25}) which leads t
\begin{equation}
E_{KG}^{dS}=\frac{mc^{2}\sqrt{1-\frac{\hbar ^{2}\lambda }{m^{2}c^{2}}\left[
\left( N-\ell -\frac{1}{2}+\sqrt{\left( \ell +\frac{1}{2}\right) ^{2}-\left(
Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right) ^{2}-\ell \left( \ell
+1\right) -1\right] }}{\sqrt{1+\frac{Z^{2}\mu ^{2}}{\left( N-\ell -\frac{1}{
}+\sqrt{\left( \ell +\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}
\right) ^{2}}}},  \label{26}
\end{equation}
where $N=n+\ell +1$ is the principal quantum number. We observe that the
energy levels depend on the deformation parameter $\lambda $. This is a
natural consequence of the modified Heisenberg algebra. We also note that
the energy levels depend on $N^{2}$, which is the feature of hard
confinement. According to the energy levels, we remark the following:

\begin{itemize}
\item The constraint $\ell +\frac{1}{2}\geqslant Z\mu $ is necessary for the
existence of physical energy eigenvalues.

\item For $\ell =0,$ we must impose $Z\leqslant 69$ and bound states do not
exist for larger $Z$-values.

\item For larger $N$-values, the energy spectrum would have an unphysical
behavior.
\end{itemize}

The expansion of Eq.(\ref{26}) up to the first order in $\lambda$ yield
\begin{equation}
E_{KG}^{dS}=\varepsilon _{KG}-\frac{\hbar ^{2}\lambda \varepsilon _{KG}}
2m^{2}c^{2}}\left[ \left( N-\ell -\frac{1}{2}+\sqrt{\left( \ell +\frac{1}{2
\right) ^{2}-\left( Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right)
^{2}-\ell \left( \ell +1\right) -1\right] ,  \label{27}
\end{equation}
where,
\begin{equation}
\varepsilon _{KG}=mc^{2}\left[ 1+\frac{Z^{2}\mu ^{2}}{\left( N-\ell -\frac{
}{2}+\sqrt{\left( \ell +\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}
\right) ^{2}}\right] ^{-\frac{1}{2}}.
\end{equation}
The first term in (\ref{27}) is the energy spectrum of the ordinary
three-dimensional Coulomb potential of spin-0 particles with no deformation,
while the second term represents the correction due to the presence of the
EUP. Expanding (\ref{27}) in powers of $\left( Z\mu \right) $ yields
\begin{eqnarray}
W_{KG}^{ds} &=&E_{KG}^{dS}-mc^{2}=-\frac{mZ^{2}e^{4}}{2\hbar ^{2}N^{2}}
\frac{\hbar ^{2}\lambda }{2m}\left[ N^{2}-\ell \left( \ell +1\right) -
\right] -mc^{2}\frac{Z^{4}\mu ^{4}}{2N^{4}}\left( \frac{N}{\ell +\frac{1}{2}
-\frac{3}{4}\right) \left \{ 1-\frac{\hbar ^{2}\lambda }{2m^{2}c^{2}}\left[
N^{2}-\ell \left( \ell +1\right) -1\right] \right \}  \notag \\
&&+\frac{\hbar ^{2}\lambda }{2m}\frac{\left( Z\mu \right) ^{2}}{2N^{2}}\left
\{ \left[ \frac{2N^{3}}{\left( \ell +\frac{1}{2}\right) }-N^{2}-\ell \left(
\ell +1\right) -1\right] +\left( Z\mu \right) ^{2}\left[ 1+\frac{N^{3}}
2\left( \ell +\frac{1}{2}\right) ^{3}}-\frac{N^{2}}{2\left( \ell +\frac{1}{2
\right) ^{2}}-\frac{N}{\left( \ell +\frac{1}{2}\right) }\right] \right \} .
\label{29}
\end{eqnarray
The first and the second terms in (\ref{29}) represent the non-relativistic
energy levels of hydrogen in dS space \cite{35}, while the other terms are
relativistic corrections in dS space.

The same calculation can be performed for the case of anti-de Sitter space
by taking the change of the sign in the deformation into the account by
using $\lambda>0$. The energy spectrum of the system is found as
\begin{equation}
E_{KG}^{AdS}=\frac{mc^{2}\sqrt{1+\frac{\hbar ^{2}\lambda }{m^{2}c^{2}}\left[
\left( N-\ell -\frac{1}{2}+\sqrt{\left( \ell +\frac{1}{2}\right) ^{2}-\left(
Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right) ^{2}-\ell \left( \ell
+1\right) -1\right] }}{\sqrt{1+\frac{Z^{2}\mu ^{2}}{\left( N-\ell -\frac{1}{
}+\sqrt{\left( \ell +\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}
\right) ^{2}}}}.
\end{equation}
We can plot our results for different scenarios. The contribution of the
deformation is very small numerically for physical values of the parameters.
Thus we take $\hbar=c=m=1$ in order to avoid numerical errors and make the
effect of the deformation factor visible in the graphics. In Fig. (\re
{fig:fig1}) we plot the ratio $\frac{E_{KG}^{(A)dS}}{\varepsilon_{KG}}$ with
respect to $N$ for some values of the deformation parameter $\lambda$. Here,
$\ell=0$ and $Z=50$. We see that the curves for the AdS case grow with $N$,
while they decrease almost rapidly with $N$ in the dS case. The undeformed
calculation shown with a solid line with $\lambda=0$ gives the ratio as
unity as expected.

The Figures (\ref{fig:fig2}) and (\ref{fig:fig3}) show the behavior of the
energy eigenvalues $E_{KG}^{(A)dS}$ with respect to $Z$. We take $N=1$ and
\ell=0$ in Fig. (\ref{fig:fig2}). As we have calculated above, no bound
states exist for $Z>69$. In Fig. (\ref{fig:fig3}), for $N=3$ and $\ell=1$,
we verify the condition $\ell +\frac{1}{2}\geqslant Z\mu$ graphically by
having $Z=206$ as the accumulation point.
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.7]{fig1_KG_rate}
\caption{$\frac{E_{KG}^{(A)dS}}{\protect \varepsilon_{KG}}$ vs. $N$}
\label{fig:fig1}
\end{figure}
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.7]{fig2_KG_N1L0}
\caption{$E_{KG}^{(A)dS}$ vs. $Z$ for $N=1$, $\ell=0$}
\label{fig:fig2}
\end{figure}
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.7]{fig3_KG_N3L1}
\caption{$E_{KG}^{(A)dS}$ vs. $Z$ for $N=3$, $\ell=1$}
\label{fig:fig3}
\end{figure}

\section{Dirac Equation for the Hydrogen Atom}

The Dirac equation in the presence of the Coulomb potential $V$ i
\begin{equation}
\left[ c\overrightarrow{\mathbf{\alpha }}\overrightarrow{\cdot P}+\beta
mc^{2}-E+V\right] \psi =0,  \label{31}
\end{equation}
where the matrices $\mathbf{\alpha }$ and $\beta $ satisfy the
anticommutation relations
\begin{equation}
\left \{ \mathbf{\alpha }_{i},\beta \right \} =0;\text{ \  \ }\left \{
\mathbf{\alpha }_{i},\mathbf{\alpha }_{j}\right \} =2\delta _{ij};\text{ \  \
}i,j=1,2,3.
\end{equation}
An explicit familiar representation of\ $\mathbf{\alpha }$\ and $\beta $\ is
provided b
\begin{equation}
\mathbf{\alpha }_{i}=\left(
\begin{array}{cc}
0 & \sigma _{i} \\
\sigma _{i} &
\end{array
\right) ;\text{ \  \ }\beta =\left(
\begin{array}{cc}
1 & 0 \\
0 & -
\end{array
\right) ,
\end{equation}
where $\sigma _{i}$ are $2 \times 2$ Pauli spin matrices. In spherical
coordinates, the operator $\overrightarrow{\mathbf{\alpha }}\overrightarrow
\cdot P}$ can be written a
\begin{equation}
\overrightarrow{\mathbf{\alpha }}\overrightarrow{\cdot P}=\sqrt{1+\lambda
r^{2}}\overrightarrow{\mathbf{\alpha }}\overrightarrow{\cdot p}=-i\hbar
\sqrt{1+\lambda r^{2}}\mathbf{\alpha }_{r}\left( \frac{\partial }{\partial r
+\frac{1}{r}-\frac{\beta }{\hbar r}\boldsymbol{K}\right) ,
\end{equation}
in the deformed case. Here,
\begin{equation}
\mathbf{\alpha }_{r}=\overrightarrow{\mathbf{\alpha }}\overrightarrow{\cdot
};\text{ \  \  \ }\boldsymbol{K}=\beta \left( \overrightarrow{\sum }\cdot
\overrightarrow{\mathbf{L}}+\hbar \right) ;\text{ \ }\overrightarrow{\sum
=\left(
\begin{array}{cc}
\overrightarrow{\sigma } & 0 \\
0 & -\overrightarrow{\sigma
\end{array
\right) ,
\end{equation
where the last operator is absent in the Klein-Gordon equation. The solution
ansatz of (\ref{31}) can be chosen such that
\begin{equation}
\psi =\left(
\begin{array}{c}
f_{1}\left( r\right) \mathcal{Y}_{\kappa ,\nu }\left( \theta ,\varphi \right)
\\
if_{2}\left( r\right) \mathcal{Y}_{-\kappa ,\nu }\left( \theta ,\varphi
\right
\end{array
\right) ,
\end{equation}
where $\mathcal{Y}_{\kappa ,\nu }\left( \theta ,\varphi \right) $ are spinor
spherical harmonics. Considering the action of the operator $\boldsymbol{K}
, we have
\begin{eqnarray}
\boldsymbol{K}\mathcal{Y}_{\kappa ,\nu }\left( \theta ,\varphi \right)
&=&-\hbar \kappa \mathcal{Y}_{\kappa ,\nu }\left( \theta ,\varphi \right) ,
\notag \\
\boldsymbol{K}\mathcal{Y}_{-\kappa ,\nu }\left( \theta ,\varphi \right)
&=&\hbar \kappa \mathcal{Y}_{-\kappa ,\nu }\left( \theta ,\varphi \right) ,
\end{eqnarray}
where the quantum number $\kappa$ is defined a
\begin{equation}
\kappa =\pm \left( j+\frac{1}{2}\right) =\left \{
\begin{array}{c}
-\left( \ell +1\right) \text{ \  \  \  \ for }j=l+1/2 \\
\ell \text{ \  \  \  \  \  \  \  \  \  \  \  \  \  \  \ for }j=l-1/
\end{array
\right. .
\end{equation}
Using the expression for $\overrightarrow{\mathbf{\alpha }}\overrightarrow
\cdot P}$ we can rewrite Eq. (\ref{31}) as
\begin{equation}
\left[ -i\hbar c\sqrt{1+\lambda r^{2}}\mathbf{\alpha }_{r}\left( \frac
\partial }{\partial r}+\frac{1}{r}-\frac{\beta }{\hbar r}\boldsymbol{K
\right) +\beta mc^{2}-E+V\right] \psi =0.
\end{equation
From this equation, we get two coupled differential equations
\begin{equation}
\left( \frac{E-mc^{2}}{\hbar c}+Z\mu \frac{\sqrt{1+\lambda r^{2}}}{r}\right)
f_{1}\left( r\right) =\sqrt{1+\lambda r^{2}}\left( \frac{\kappa -1}{r}-\frac
d}{dr}\right) f_{2}\left( r\right) ,  \label{40}
\end{equation
\begin{equation}
\left( \frac{E+mc^{2}}{\hbar c}+Z\mu \frac{\sqrt{1+\lambda r^{2}}}{r}\right)
f_{2}\left( r\right) =\sqrt{1+\lambda r^{2}}\left( \frac{\kappa +1}{r}+\frac
d}{dr}\right) f_{1}\left( r\right) .  \label{41}
\end{equation}
These two equations can be solved exactly by a diagonalization procedure
\cite{36},
\begin{equation}
\left(
\begin{array}{c}
g_{1} \\
g_{2
\end{array
\right) =\left(
\begin{array}{cc}
1 & X \\
X &
\end{array
\right) \left(
\begin{array}{c}
f_{1} \\
f_{2
\end{array
\right) ,
\end{equation
where $X=\frac{\gamma -\kappa }{Z\mu }$ and $\gamma =\sqrt{\kappa
^{2}-\left( Z\mu \right) ^{2}}$. which transforms Eqs. (\ref{40}) and (\re
{41}) into the following equations,
\begin{equation}
\left[ \sqrt{1+\lambda r^{2}}\frac{d}{dr}+\left( \gamma +1\right) \frac
\sqrt{1+\lambda r^{2}}}{r}-\frac{Z\mu }{\gamma }\frac{E}{\hbar c}\right]
g_{1}=\left[ \frac{mc^{2}}{\hbar c}+\frac{\kappa }{\gamma }\frac{E}{\hbar c
\right] g_{2},
\end{equation
\begin{equation}
\left[ \sqrt{1+\lambda r^{2}}\frac{d}{dr}+\left( 1-\gamma \right) \frac
\sqrt{1+\lambda r^{2}}}{r}+\frac{Z\mu }{\gamma }\frac{E}{\hbar c}\right]
g_{2}=\left[ \frac{mc^{2}}{\hbar c}-\frac{E}{\hbar c}\frac{\kappa }{\gamma
\right] g_{1}.
\end{equation}
This system gives the following differential equation for the component
g_{2}\left( r\right) =\frac{1}{\sqrt{r}}\Xi \left( r\right) ,
\begin{equation}
\left[ \left( 1+\lambda r^{2}\right) \left( \frac{d^{2}}{dr^{2}}+\frac{1}{r
\frac{d}{dr}\right) +\lambda r\frac{d}{dr}-\frac{\left( \gamma -\frac{1}{2
\right) ^{2}}{r^{2}}+\frac{2Z\mu E}{\hbar c}\frac{\sqrt{1+\lambda r^{2}}}{r}
\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}}-\lambda \left( \gamma ^{2}-\frac{1}
4}\right) \right] \Xi \left( r\right) =0.
\end{equation}
Following the same procedure in the Klein-Gordon case, the solution is
obtained as by
\begin{equation}
\Xi =y^{a_{1}}\left( 1-y\right) ^{b_{1}}\mathbf{F}\left( A_{1};B_{1};\frac{
}{2}+2a,y\right) ,
\end{equation
with $\mathbf{F}$ being a hypergeometric function with the parameter
\begin{equation}
A_{1}=a_{1}+b_{1}-\left( \gamma -\frac{1}{2}\right) ;\text{ \
B_{1}=a_{1}+b_{1}+\left( \gamma -\frac{1}{2}\right) ,
\end{equation}
wher
\begin{equation}
a_{1}=\frac{1}{4}+\frac{1}{2}\sqrt{\gamma ^{2}-\frac{2\mu ZE}{\hbar c\sqrt
\lambda }}-\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}\lambda }};\text{ \  \
b_{1}=\frac{1}{4}+\frac{1}{2}\sqrt{\frac{2\mu ZE}{\hbar c\sqrt{\lambda }
+\gamma ^{2}-\frac{E^{2}-m^{2}c^{4}}{\hbar ^{2}c^{2}\lambda }}.
\end{equation}
If $A_{1}=-n$ or $B_{1}=-n,$ ($n=0,1,2,...$), the hypergeometric function
reduces to a polynomial in $y$ whose degree is $n,$ and then we hav
\begin{equation}
\gamma +\frac{1}{2}\sqrt{\gamma ^{2}+\frac{m^{2}c^{4}}{\hbar
^{2}c^{2}\lambda }-\frac{2\mu ZE}{\hbar c\sqrt{\lambda }}-\frac{E^{2}}{\hbar
^{2}c^{2}\lambda }}+\frac{1}{2}\sqrt{\gamma ^{2}+\frac{m^{2}c^{4}}{\hbar
^{2}c^{2}\lambda }+\frac{2\mu ZE}{\hbar c\sqrt{\lambda }}-\frac{E^{2}}{\hbar
^{2}c^{2}\lambda }}=-n.  \label{49}
\end{equation
We can obtain the energy eigenvalues by solving this equation for $E$,
namely,
\begin{equation}
E_{Dirac}^{dS}=\frac{mc^{2}\sqrt{1-\frac{\hbar ^{2}\lambda }{m^{2}c^{2}
\left[ \left( N-j-\frac{1}{2}+\sqrt{\left( j+\frac{1}{2}\right) ^{2}-\left(
Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right) ^{2}-\left( j+\frac{1}{2
\right) ^{2}\right] }}{\sqrt{1+\frac{\mu ^{2}Z^{2}}{\left( N-j-\frac{1}{2}
\sqrt{\left( j+\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}}\right) ^{2}
}},  \label{50}
\end{equation}
where $N=n+j+\frac{1}{2}$ is the principal quantum number. The equation (\re
{50}) gives the energy levels of hydrogen-like atoms in de Sitter space. The
energy levels depend on the principal quantum number $N$, $j$, $Z$ and the
deformation parameter $\lambda $. It should be emphasized that the energy
depends on the quantum number $j$, which is associated with both orbital
angular momentum and spin. The other thing to notice about Eq. (\ref{50}) is
that for states with $N=1$ and $j=1/2,$ the energy spectrum is given by,
\begin{equation}
E_{Dirac}^{dS}=mc^{2}\sqrt{1-\left( Z\mu \right) ^{2}}.
\end{equation
In this special limit, it can be easily seen that the effects of the
deformation have been totally disappeared and, if $\left( Z\mu \right) =1,$
the energy becomes zero, i.e. $E_{N}^{ds}=0$.

In addition, if $Z\mu >j+\frac{1}{2}$ the energy levels in (\ref{50}) become
complex which means that there exists no regular polynomial solutions for
ns_{1/2}$ or $np_{1/2}$ states when the charge is greater than $Z>137$.

Expanding Eq.(\ref{50}) to the first order in $\lambda $, we obtai
\begin{equation}
E_{Dirac}^{dS}=\varepsilon _{Dirac}-\frac{\hbar ^{2}\lambda \varepsilon
_{Dirac}}{2m^{2}c^{2}}\left[ \left( N-j-\frac{1}{2}+\sqrt{\left( j+\frac{1}{
}\right) ^{2}-\left( Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right)
^{2}-\left( j+\frac{1}{2}\right) ^{2}\right] ,  \label{52}
\end{equation}
wher
\begin{equation}
\varepsilon _{Dirac}=mc^{2}\left[ 1+\frac{\mu ^{2}Z^{2}}{\left( N-j-\frac{1}
2}+\sqrt{\left( j+\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}}\right)
^{2}}\right] ^{\frac{-1}{2}}.
\end{equation}
Cleary, the first term is identical with the Dirac energy levels in the
ordinary case. The second term represents the correction due to the presence
of the extended uncertainty principle. Moreover, the series expansion of
\ref{52}) in powers of $\left( Z\mu \right) $ read
\begin{equation}
W_{Dirac}^{ds}=E_{N}^{dS}-mc^{2}=\epsilon _{N;j}+\Delta \mathcal{E}_{N;j},
\label{54}
\end{equation
where
\begin{equation}
\epsilon _{N;j}=-\frac{Z^{2}e^{4}m}{2\hbar ^{2}N^{2}}-mc^{2}\frac{\mu
^{4}Z^{4}}{2N^{4}}\left( \frac{N}{\left( j+\frac{1}{2}\right) }-\frac{3}{4
\right).
\end{equation}
Here, the first term is the energy spectrum of the non-relativistic hydrogen
atom, the second term contains all of the details of the fine structure, an
\begin{equation}
\Delta \mathcal{E}_{N;j}=-\frac{\hbar ^{2}\lambda }{2m}\left[ 1-\frac
Z^{2}\mu ^{2}}{2N^{2}}-\frac{\mu ^{4}Z^{4}}{2N^{4}}\left( \frac{N}{j+\frac{
}{2}}-\frac{3}{4}\right) \right] \left[ N^{2}-\left( j+\frac{1}{2}\right)
^{2}-\left( Z\mu \right) ^{2}\left( 1+\frac{\left( Z\mu \right) ^{2}}
4\left( j+\frac{1}{2}\right) ^{2}}\right) \left( \frac{N}{j+\frac{1}{2}
-1\right) \right].
\end{equation}
The formula (\ref{54}) shows the effect of the EUP on the non-relativistic
energy levels for the one-electron atom. We observe that the EUP correction
carries new terms associated with the relativistic correction, which do not
exist in the undeformed case.

Consequently, we can calculate the electron energies of hydrogen-like atoms
in de Sitter space using our results with the numerical values of
mc^{2}=511004.1\unit{eV}$ and $\sqrt{\lambda }=0.252\times 10^{6}\unit{m
^{-1}$ \cite{28,37}$.$ The results are given in Table 1.

\begin{center}
\bigskip
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$N$ & $\ell $ & $j$ & Label & $\epsilon _{N;j}$ \ ($\unit{eV}$) & $\left
\vert \Delta \mathcal{E}_{N;j}\right \vert $ \ ($\unit{eV}$) \\ \hline
1 & 0 & 1/2 & $1s_{1/2}$ & $-13.605$ & $0$ \\ \hline
2 & 0 & 1/2 & $2s_{1/2}$ & $-3.40132$ & $3.\, \allowbreak 415\,0\times
10^{-8} $ \\ \hline
2 & 1 & 1/2 & $2p_{1/2}$ & $-3.40132$ & $3.\, \allowbreak 415\,0\times
10^{-8} $ \\ \hline
2 & 1 & 3/2 & $2p_{13/2}$ & $-3.40127$ & $0$ \\ \hline
3 & 0 & 1/2 & $3s_{1/2}$ & $-1.51169$ & $1.\, \allowbreak 940\,5\times
10^{-8} $ \\ \hline
3 & 1 & 1/2 & $3p_{1/2}$ & $-1.51169$ & $1.\, \allowbreak 940\,5\times
10^{-8} $ \\ \hline
3 & 1 & 3/2 & $3p_{3/2}$ & $-1.51168$ & $1.\, \allowbreak 212\,8\times
10^{-8} $ \\ \hline
3 & 2 & 3/2 & $3d_{3/2}$ & $-1.51168$ & $1.\, \allowbreak 212\,8\times
10^{-8} $ \\ \hline
3 & 2 & 5/2 & $3d_{5/2}$ & $-1.51167$ & $0$ \\ \hline
\end{tabular}

\begin{tabular}{l}
Table 1: Energy levels of hydrogen-like atoms
\end{tabular}
\end{center}

The same calculation can be performed for the case of anti-de Sitter space.
According to the correspondence $\lambda \rightarrow -\lambda $, the energy
levels of a spin-1/2 particle in a Coulomb potential in anti-de Sitter space
can be written as
\begin{equation}
E_{Dirac}^{AdS}=\frac{mc^{2}\sqrt{1+\frac{\hbar ^{2}\lambda }{m^{2}c^{2}
\left[ \left( N-j-\frac{1}{2}+\sqrt{\left( j+\frac{1}{2}\right) ^{2}-\left(
Z\mu \right) ^{2}}\right) ^{2}+\left( Z\mu \right) ^{2}-\left( j+\frac{1}{2
\right) ^{2}\right] }}{\sqrt{1+\frac{\mu ^{2}Z^{2}}{\left( N-j-\frac{1}{2}
\sqrt{\left( j+\frac{1}{2}\right) ^{2}-\left( Z\mu \right) ^{2}}\right) ^{2}
}}.
\end{equation}
We can plot our results as in the Klein-Gordon case, following the same
numerical procedure. We observe the same behavior in the energy curves.

In Fig. (\ref{fig:fig4}) we plot the ratio $\frac{E_{Dirac}^{(A)dS}}
\varepsilon_{Dirac}}$ with respect to $N$ for some values of $\lambda$. We
see that the curves for the AdS case grow with $N$, while they decrease with
$N$ in the dS case. The undeformed energy value corresponding to $\lambda=0$
is shown with a solid line where $E_{Dirac}^{(A)dS}=\varepsilon_{Dirac}$.

The Figures (\ref{fig:fig5}) and (\ref{fig:fig6}) show the behavior of the
energy eigenvalues $E_{Dirac}^{(A)dS}$ with respect to $Z$. In Fig. (\re
{fig:fig5}) we take $N=2$ and $j=1/2$ and using $Z \mu>j+\frac{1}{2}$, we
see that the bound states are limited by $Z<137$. The results are similar in
Fig. (\ref{fig:fig6}) where $N=4$, $j=3/2$ and $Z<274$.
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.5]{fig4_Dirac_rate}
\caption{$\frac{E_{Dirac}^{(A)dS}}{\protect \varepsilon_{Dirac}}$ vs. $N$}
\label{fig:fig4}
\end{figure}
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.5]{fig5_Dirac_N2j12}
\caption{$E_{Dirac}^{(A)dS}$ vs. $Z$ for $N=2$, $j=1/2$}
\label{fig:fig5}
\end{figure}
\begin{figure}[tbph]
\centering
\includegraphics[scale=0.5]{fig6_Dirac_N4j32}
\caption{$E_{Dirac}^{(A)dS}$ vs. $Z$ for $N=4$, $j=3/2$}
\label{fig:fig6}
\end{figure}

\section{Conclusion}

We studied the Klein-Gordon and Dirac equations for the relativistic Coulomb
potential in the framework of the extended uncertainty principle for de
Sitter and anti-de Sitter spaces. We treated the problem analytically and
obtained the energy spectra and the eigenfunctions exactly in both cases.
Eventually, we obtained the relativistic bound-state energy spectra for
hydrogenic atoms and the corresponding wave functions for the spin $0$ and
1/2$ cases.

We solved the Klein-Gordon and Dirac equations in terms of the
hypergeometric functions and utilizing the conditions that truncate the
series to yield a polynomial solution, we obtained the energy eigenvalues.
Analyzing the energy spectra, we found the limits $\ell +\frac{1}{2
\geqslant Z\mu $ and $Z\mu <j+\frac{1}{2}$ which are necessary for
the existence of physical energy eigenvalues in the Klein-Gordon and Dirac
cases, respectively.

Furthermore, we used our analytical results to create a numerical table for
the energy levels of hydrogen-like atoms and plot some graphics to present
the effects of the deformation on the energy spectra and the accumulation of
the curves to a certain $Z$-value in a visual way for de Sitter and anti-de
Sitter spaces.

redpajama_set_name: RedPajamaArXiv


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text:
Net-Zero Trucks? Yes, It's Possible.
The trucks used in industries like mining and agriculture burn diesel and emit a lot of CO2. Fortunately, replacement solutions exist—if companies understand the costs and benefits.
Heavy industries like mining and agriculture are making ambitious commitments to reduce their greenhouse gas emissions. But the diesel truck fleets these companies use—everything from 300-ton haulers at mining sites to18-wheel tractor trailers on highways—are a primary source of CO2. These vehicles all burn diesel, making up a large share of the industries' overall environmental footprint. Unless companies commit to eliminating or reducing diesel fuel, they simply won't hit their net-zero targets.
We recently analyzed alternative fuels to determine how they could perform in a range of trucks and applications. The key takeaway? It's not easy to displace diesel in transportation and logistics or in other industries requiring heavy equipment, but it is possible, through two broad options that companies can apply individually or together:
Speed and Ease—but at a Cost. Companies that want to make a change today can implement a straightforward switch to sustainable biodiesel using the same vehicle fleets and infrastructure, provided they are willing to pay higher fuel costs.
Lower Cost but Greater Complexity and Time Requirements. Companies that want to keep costs low can eliminate diesel, but the process will take longer, be more complex, and rely on new technology for alternative fuels, infrastructure, and vehicles.
A global mining company weighed these two options for its fleet and proactively engaged with its OEM and energy suppliers to understand which technologies were technically feasible and commercially viable. It determined that it could remove more than 6 megatons of CO2 per year, 20 years earlier than planned—equal to eliminating nearly 1.5 million passenger cars.
Companies don't have to wait until 2050 to eliminate diesel. In fact, if they are serious about combating climate change, they can't wait.
Why Diesel Is Hard to Replace
Diesel is widely used in heavy industries for good reason: it's cheap, energy dense, and readily available through established infrastructure. Different applications and industries have individualized operational requirements—variable payloads and distances, whether they're used on or off roads—but diesel is a universally applicable fuel.
Because it is relied on across so many industries, diesel combustion represents a huge share of overall emissions, comprising up to 40% of all CO2 emissions for mining and 35% for agriculture. Moreover, replacing diesel is challenging, requiring a systems-level approach that includes not just different types of fuel but also new powertrains and onboard fuel systems. Companies must also consider all the fuel infrastructure—like pipelines, storage tanks, and refueling and recharging stations—that will need to be upgraded.
Fortunately, several diesel alternatives exist already, and others are under development. Each presents tradeoffs for fleet operators, but the benefits can be striking. In particular, there are four alternatives that companies should consider. (See the exhibit.)
Green Electricity. One potential fuel source is energy derived from renewable sources such as wind and solar. Green electricity can be used directly or utilized to power the industrial processes required to generate other alternative fuels. Battery electric power generated from renewable sources is viable for privately owned passenger cars, which often sit unused for a portion of a given day. They are therefore easy to charge and don't operate at anywhere near their payload limit (meaning heavy batteries aren't an issue). By contrast, the weight of the battery and recharging time needed for heavy equipment and vehicles—and their need to operate close to their maximum payload and operate for long periods between recharging—makes battery electric power a more challenging option.
Some workarounds offer niche solutions. For example, heavy vehicles that operate on highly predictable routes—such as deep-pit mining trucks—can be powered through overhead electrical cables that remain in direct contact with the vehicle, similar to the light-rail systems used in some cities. Where it works, this is a great solution. However, it won't work everywhere or for all vehicles, and installing the power lines requires additional capital investment.
Green Hydrogen. Hydrogen can be produced using water as a feedstock through an industrial process known as electrolysis. If that process is powered by renewable energy sources such as wind or solar, the result is carbon-neutral ("green") hydrogen, which can be burned in specialized internal combustion engines or used to power hydrogen fuel cells. Fuel cell passenger vehicles are available today and provide longer ranges and faster refueling than electric vehicles, making them a preferred solution for long-haul trucking on highways. However, hydrogen is significantly less energy dense than sustainable biofuels and e-diesel (which means that it requires a larger fuel tank and longer refueling times than diesel) and therefore presents challenges for vehicles or equipment where productivity and payload matter.
Sustainable Biofuels. A range of sustainable biofuels are entering the market, including hydrotreated vegetable oil (HVO), which is produced by processing waste vegetable oils or animal fats, and green diesel, which is produced by processing biomass waste such as crop residues, wood, and sawdust. Both can replace diesel in current fleets without requiring changes to engines or storage infrastructure, but they are currently far more expensive than diesel. They can, however, reduce emissions by up to 90%. (They do not fully eliminate emissions because they still require some energy to produce, but the bulk of their carbon footprint has already been accounted for in other industry lifecycles.)
In addition to cost, sustainable biofuels present two challenges. The first is the importance of ensuring that feedstocks are ethically sourced (to maintain a sustainable and net-positive outcome), although some systems are emerging to provide "traceability" guarantees to end users. The second is supply. Production is forecast to reach 570 million barrels by 2030, but that only accounts for a small proportion of the diesel consumed in mining, agriculture, and road freight. What's more, other hard-to-abate industries increasingly compete for the same feedstock that is used for HVO (such as the aviation industry's growing demand for sustainable fuel), so supplies will almost certainly be constrained.
E-diesel. A carbon-neutral synthetic form of diesel, e-diesel can be produced from carbon dioxide, water, and renewable energy. Producing it at scale should be possible as soon as the early 2030s, and e-diesel is unlikely to face the same scale issues as sustainable biofuel, since the feedstocks—carbon dioxide, water, and renewable energy—are more readily available. E-diesel is a straightforward solution for OEMs and vehicle operators, because it is compatible with current internal combustion engines and infrastructure. However, like HVO and green diesel, it is forecast to cost twice as much as diesel in 2030.
Overall, most green electricity and green hydrogen solutions will require more frequent refueling, larger fuel tanks, or both. In addition, there is an inverse relationship between CO2 performance and operational complexity. The solutions that have a lower cost per ton of CO2 abated will likely be more difficult to implement. Hydrogen fuel cells are a good example. The technology holds significant promise as a way to virtually eliminate CO2 emissions—assuming the production processes are powered by renewable energy—but it would also require completely new engine designs and infrastructure for distribution, storage, and refueling.
Two Potentials Path Forward
To understand what's possible in terms of technology and commercial viability, we recently analyzed the range of alternate energy sources and weighed them across four criteria: operational complexity, fuel performance, financial considerations (including capex, opex, and fleet replacement cycles), and overall environmental performance. We also talked to vehicle OEMs, engine manufacturers, oil and gas companies, governments, and fleet operators in a range of industries: mining, agriculture, and logistics.
Based on that analysis, we believe the transition away from diesel is possible and that it can be done faster than conventional wisdom might suggest—provided that companies can make well-informed tradeoffs. They can choose from two paths: either move rapidly away from diesel but pay more initially or migrate more gradually to alternative fuel sources but deal with more complexity.
Speed and Ease—but at a Cost. Companies that want to move away from diesel immediately can transition to biofuel that is ethically sourced. Biofuels such as HVO or green diesel are available today and can be used in existing vehicle engines, requiring no changes to fleets or infrastructure and limited transition of the workforce. This approach allows companies to generate environmental gains starting today.
The catch with this approach is cost: HVO is two to four times more expensive than diesel. That difference will likely shrink over time, due to scale effects and other efficiencies, along with increased incentives, taxes, and regulations in some markets, but it still presents a challenge for companies that want to take immediate action.
Lower Cost but Greater Complexity and Time Requirements. With the right collaboration between energy producers and vehicle OEMs, net-zero solutions for heavy trucks will be commercially available in the next 10 to 15 years. Between now and then, companies can begin to implement these solutions as they become available, but they will likely need to accept increased complexity in several dimensions.
First, if the goal is lowest cost, companies probably won't be able to use a single fuel for all vehicles and all applications. For example, battery electric power will be an option for light-utility trucks or pickups, but companies will need other solutions such as hydrogen fuel cells for heavier vehicles.
In addition, companies need to assess risks by asking some critical questions: which technologies are field tested and proven, which fuel supply chains are secure, and how can refueling downtime be minimized? They will also need to understand the cost implications of different technologies, along with timing: which technologies will be ready, how will costs for innovative technologies decline over time, and can those solutions be synchronized to fleet replacement cycles?
For companies that can manage these complexities, there is a clear competitive advantage to being first to market: they may be able to charge a price premium to customers for products that are truly green.
Notably, these two paths are not mutually exclusive. Different organizations may opt to apply both approaches depending on their timeline, operational requirements, and other factors.
(Courtesy Boston Consulting Group)
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HiLight today announce the release of the first of a family of new CMOS 'COMBO' ICs for 10Gb PON applications.
The family will be demonstrated at CIOE in Shenzhen in September. Please contact us to arrange a private viewing.


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Home Entertainment How a Show About Sex Work Became One of the Most Sex-Positive...
How a Show About Sex Work Became One of the Most Sex-Positive on TV
By Carita Rizzo
Courtesy Starz
In directing material that is sexual in nature, Lodge Kerrigan's goal is not to get you off. "I've directed a lot of sex scenes," says the co-creator of The Girlfriend Experience, Starz's lauded, Golden Globe-nominated anthology series about female escorts, which just kicked off its second season. "When I direct a scene, I direct the sub-text of the scene. If there's no subtext, then it's just titillation, and I have no interest in doing that."
The drama, based on Steven Soderbergh's 2009 indie film with Sasha Grey about the day-to-day life of an escort, continues to tackle individual struggles set against the backdrop of high-end prostitution. But for Kerrigan and series co-creator Amy Seimetz, exaggerating the business of sex—controversial as it still may be—feels pedestrian. "Inherently, within the world of escorting itself, there is nothing particularly dramatic about it," says Kerrigan. "It's an act. You pay some money. You get something. It's like getting a haircut."
Seimetz and Kerrigan don't take stand for or against sex work. Instead, they've decided to treat it as a trade that simply exists. "We approached it in this non-judgmental space, of not either glorifying or saying that sex working is bad," says Seimetz. "We knew that was going to be a topic of conversation. And as filmmakers coming from the world of independent film, that is always what you hope; that there is some dialogue and some sort of confrontation happening."
Diverting from the first season, which starred Riley Keough as a law student entering the complex world of transactional relationships, season two consists of two storylines with no overlap save for the show's broader themes related to the two lead characters' profession, which is abbreviated simply to "the GFE."
Sex work is a huge, broad spectrum. There are some dark, dark sides to it. That's not what we're doing.
The idea, as with the popular anthology series Black Mirror, is to play with the structure of TV to determine whether audiences can create links between two distinct narratives based on context alone. "If you had two separate story lines still dealing with some thematic mirroring, it would provide a really interesting opportunity for an audience to be able to watch either of the story lines or both of them, and make their own connections," says Kerrigan. "There are certain themes that come up, particularly power dynamics, and issues of control."
Kerrigan's installment centers on a Republican super-PAC finance director (Anna Friel) who enlists the help of a young escort at the top of her game (Louisa Krause) to blackmail somebody who controls a donor list. The two women soon cross over from their professional relationship into a sexual one. "I was interested in when two people become involved, when they become intimate, how the power balance is constantly shifting, and we examine that through their sexuality," says Kerrigan.
The director sees the dynamic between the two women as something more complicated than a romance. "I think [Krause's character] becomes emotionally vulnerable," he says. "When you first start to become emotionally vulnerable to somebody else, you're giving up some degree of power. What I wanted to do was try to track the variations of the journey of that power dynamic in a relationship."
Seimetz's piece deals with a former GFE provider, played by Carmen Ejogo, who has to go into witness protection in New Mexico where she struggles with her sense of self. "That new identity isn't appealing to her because it's not glamorous enough, so she starts dabbling in the lifestyle of GFE while she is under witness protection," says Seimetz, who wanted to explore the idea of a clean slate. "If you want to draw parallels to being a GFE, it's that you can be anyone you want to be, so when you have this opportunity to enter witness protection and actually recreate your life, you can recreate whoever you are," says Seimetz. "Given that opportunity, she still wants to dabble in this lifestyle."
Seimetz hopes the series continues to invite viewers to question their oftentimes strong opinions on the world's oldest profession. "In The Sopranos we have a male character who's murdering people and for some reason everyone's fine with that, but when a woman decides to sell her body, we're suddenly in territory where everyone is up in arms, saying, 'Is this feminist or not?" says Seimetz. "Can we approach the same subject matter with the objectivity that you do with something like The Sopranos or Breaking Bad?"
And while the two are not attempting to glorify the profession, the female characters in The Girlfriend Experience are not portrayed as victims of the workplace. "Sex work is a huge, broad spectrum. There are some dark, dark, dark sides to it. That's not what we're doing," says Seimetz. "These women aren't constantly walking into danger. It's actually just two human beings wanting to spend time with each other. And yes, there are sexual implications to that. Because there's a sexual implication to a lot of daily life."
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New Year's resolutions aren't just for adults! The start of the new year is a great time for parents to encourage children to talk about their feelings and set goals for the upcoming year. Parents can use this reflective time to celebrate all that their child has accomplished over the past year and help them think about how to build on those achievements in the new year. These conversations allow children to learn about the value of making goals.
Take time to let each family member share something they are proud of and something they personally want to work on.
Try to limit the number of resolutions so they feel achievable and more meaningful.
Take into account your child's age. Resolutions for a preschooler might be focused on cleaning up toys, brushing teeth and being kind to their friends. School-aged children can be more active in selecting their own goals. Resolutions for this age range may focus on telling an adult about any bullying they see at school or promising to always wear a bike helmet.
Work with each child to identify their areas for personal growth. If she's having trouble reading, consider making it a goal to read 10 minutes every day. If he struggles to keep his room clean, try resolving to spend five minutes cleaning a few times a week.
Consider making both individual and family resolutions, such as spending more quality family time together or committing to more volunteer activities.
Re-visit the resolutions throughout the year and celebrate accomplishments together. Use check-ins to remind your children that their thoughts, feelings and goals are important to you.
Regardless of your child's age, encourage them to resolve to talk to a parent or other trusted adult whenever they feel scared, lonely, stressed or confused.


text:
Tag: TEC
J. Jon Bruno: Bishop gone bad?
November 16, 2016 LaymanAmerican Anglican Council, Episcopal Diocese of Los Angeles, J. Jon Bruno, St. James Episcopal Church, TEC, The Episcopal Church
California Episcopal Bishop Jon Bruno intends to sell off the property of a congregation he once championed. Parishioners and clergy are crying foul. (By Sophia Lee, World Magazine.) Most people have never heard of J. Jon Bruno, but his saga shows what is tearing apart what once was America's most influential denomination—The Episcopal Church (TEC)—and…
The False Gospel in Gay Marriage Services
July 5, 2016 The Layman26 CommentsELCA, gay marriage, Inclusive Marriage Services:, marriage, PCUSA, Presbyterian Church (USA), S. Donald Fortson, Same-Gender Weddings, TEC, UCC
A Review of Inclusive Marriage Services: A Wedding Sourcebook By S. Donald Fortson*. Several mainline writers have collaborated on a recent book, Inclusive Marriage Services: A Wedding Sourcebook.[1] Contributors to the short volume, not surprisingly, come from denominations such as the UCC, TEC, ELCA and PCUSA – bodies that no longer confess Christian teaching on human…
Ugandan Archbishop slams US over same-sex marriage
July 8, 2015 Layman5 CommentsEpiscopal Church (USA), same-sex marriage, Stanley Ntagali, TEC, U.S. Supreme Court
Posted at New Vision. Statement by the Most Rev. Stanley Ntagali on the recent decisions to change the definition of marriage by the United States' Supreme Court and the Episcopal Church in the USA The decision of the Supreme Court of the United States of America to change the definition of marriage is grievous. There…
St. James Episcopal Church Celebrates Death in 'Bleeding Kansas'
January 8, 2015 Layman1 Commentabortion, PCUSA, PPL, Presbyterians Pro-Life, pro-choice, pro-life, TEC
January 8, 2015 Fay Voshell Reverend Mother Dawn Frankfurt just finished leading her congregation of St. James Episcopal Church of Wichita, Kansas in celebrating the birth of the baby Jesus. Carols were sung, liturgies were performed and communion taken, all in the name of the miracle baby who was sent from Heaven to save the…
Tidings of discomfort and joy
December 16, 2013 LaymanAnglicans, Christians, Diocese, Episcopal Church, scorched earth policy, TEC
By Jamie Dean CONNECTICUT, NEW YORK, and CALIFORNIA—A scorched earth policy. That's how Anglicans who have left The Episcopal Church (TEC) and its endorsement of unbiblical beliefs and actions often describe TEC's response. From depressed Binghamton, N.Y., to affluent Newport Beach, Calif., TEC leaders have fought dozens of court battles to force congregations leaving the…
Who is in a position to forgive (or redefine) sin?
October 11, 2013 CarmenFowlerLaBerge1 Commenthate, LGBT, National Cathedral, sin, TEC
In an event designed to celebrate sexual anarchy the dean of the National Cathedral in Washington D.C. sought to shame traditional Christians by alleging that the upholding of natural marriage and sexual relations confined to monogamous heterosexual unions is "sin." In a remarkably clear exchange of the revealed Truth for lies, Gary Hall called what…
TEC loses battle for Quincy
September 10, 2013 LaymanDiocese of Quincy, Illinois, neutral principles of law, TEC, The Episcopal Church
By George Conger, Anglican Ink An Illinois circuit court has rejected the national Episcopal Church's claim that it is a "hierarchical church" under law, handing down a ruling that supports the Diocese of Quincy's secession from the national church. Details of the court's ruling have yet to be analyzed by Anglican Ink, but the Illinois…


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Exit Interview: Michael Blazek
by Cardinal70 on November 12, 2013
Last year, I spent the time immediately after the season examining each player that had made an appearance in St. Louis during the season. This series was well received and so I'm bringing this idea back for the 2013 offseason. More summaries than anything, I imagine the player coming into Mike Matheny's office and having a short conference before heading home for the winter. Stats are just the ones accumulated for the Cardinals during the regular season.
This year's Exit Interview series is brought to you by Bonfyre. A large number of the United Cardinal Bloggers used Bonfyre all season long and found it a great way to interact and discuss things in a limited audience. No need to worry about some pseudo-fan crashing your Facebook conversation or trying to explain fine points in 140 characters on Twitter. Invite who you want to the group and get to talking. Share pictures as well–Bonfyre is a great way to document parties or other events, especially for folks that can't be there. Sign up today and give it a try.
Name: Michael Blazek
Season stats: 0-0, 6.97 ERA, 11 games, 10.1 IP, 10 H, 10 BB, 10 K, 1.94 WHIP
Hero/Goat: Goat 1
Overall grade: C
Positives: Blazek climbed his way up the ladder and made it to St. Louis, which is a positive in its own right. He was unscored upon in his first three outings and if you take out the two terrible outings he had, his ERA was just a shade over 2.00. He was not necessarily the most heralded of prospects, but he had a good live arm and averaged a strikeout per inning before being traded to Milwaukee for John Axford.
Negatives: The two terrible outings were doozies, as he combined for six runs in 1.2 innings in those games against Houston and Cincinnati. His command was shaky as well–many of those runs in the Houston came due to him walking three batters, including one with the bases loaded. With the other strong arms in the Cardinal pen, he was expendable.
Outlook: He was a bit more successful with the Brewers, though he still walked three in seven innings. He may need a little more minor league seasoning, but there's no obvious reason why he can't be a serviceable bullpen arm for Milwaukee in years to come.
Next Post: Offseason Journal: Day 12
Previous Post: Expect The…..Expected


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Diversity Matters at Ivie McNeill Wyatt Purcell & Diggs
September 09 22:21 2020
Largest California Black-Owned Law Firm Committed to Legal, Social Justice
LOS ANGELES – Sept. 9, 2020 – Ivie McNeill Wyatt Purcell & Diggs, the largest Black-owned law firm in California, is not only committed to helping clients and the community work toward diversity, inclusion, and social justice, the firm represents those ideals itself.
With a 77-year history, Ivie McNeill Wyatt Purcell & Diggs has seen and been part of change in both clients and the world around them, but one thing that has not changed is their commitment to diversity and differing perspectives.
"Ivie McNeill Wyatt Purcell & Diggs is owned and staffed by professionals diverse in age, background, gender, and ethnicity," said W. Keith Wyatt, a long-time partner who was recently named President and Managing Director of the firm. "Our history shows we've been on the front lines of justice for many years, not just legally, but socially as well."
Keith joined the firm in 1981 and became a Director in 1986. Prior to joining Ivie McNeill & Wyatt, Mr. Wyatt was an attorney with the Legal Aid Foundation of Los Angeles. He is also a 2018 John M. Langston Bar Association Hall of Fame Inductee.
"We're extremely proud of our commitment to diversity and inclusion," added Rodney S. Diggs, a long-time partner at Ivie McNeill Wyatt Purcell & Diggs, who has significant experience trying Civil Rights and Labor and Employment cases. "Above all, our firm has a strong belief in and commitment to giving back to our community and forging a path for those who historically have not been represented in law."
In addition to Mr. Wyatt, attorneys at Ivie McNeill Wyatt Purcell & Diggs are active members of numerous legal associations dedicated to promoting diversity in the law including the California Association of Black Lawyers, Black Women Lawyers of Los Angeles, National Bar Association, Mexican American Bar Association, Latina Lawyers Bar Association, Armenian Bar Association and Black Entertainment and Sports Lawyers Association.
Ivie McNeill Wyatt Purcell & Diggs is also committed to advancing the education of minority law students and the firm's attorneys mentor law students and serve on the alumni boards of their alma maters, including the UCLA Black Alumni Association and the Howard University Alumni Association of Greater Los Angeles.
Founded in 1943, the law firm of Ivie McNeill Wyatt Purcell & Diggs is the largest Black-owned law firm in California and one of Southern California's premier full-service law firms, representing a broad range of businesses, public entities, and individuals in a vast array of litigation matters and transactions. The firm's partners include Rickey Ivie, W. Keith Wyatt, Byron Purcell, Rodney Diggs, and Marie Maurice.
Company Name: Information Xchange Group PR
Contact Person: Shawna Charles
Address:9190 W Olympic Blvd, #111
City: Beverly Hills
Website: http://ixgpr.com/
© 2018 Copyright Best Stock Market News. All Rights reserved.


WE-Knives 617B cheap folder without having to be sure of quality!
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Your guests are sure to find a creative use for these travel candles. Designed to be convenient for travel, each features a metal case tightly fastened with a clear lid, and is adorned with an blue/green thank you sticker. These 2" diameter candles are vanilla scented.


One of the most influential modern Chinese writers and the author of Lust, Caution, Eileen Chang passed away in Los Angeles in 1995. Her works, considered to be among the best Chinese literature of the 1940s, examined the themes of marriage, family, love, and relationships in the social context of 1930s and 1940s Shanghai. After her death, Dominic Cheung, Professor Emeritus at USC, took care of her sea burial in San Pedro and set up the Eileen Chang Special Collection in the East Asian Library at USC in 1997. Cheung will discuss these experiences as a part of the lecture series titled Los Angeles and Shanghai:The USC Nexus.
Please join the USC U.S.-China Institute for a book talk with journalist and author Leta Hong Fincher. Betraying Big Brother is a story of how the feminist movement in China against patriarchy could reconfigure the country and the rest of the world.
Through interviews with the Feminist Five and other leading Chinese activists, Hong Fincher illuminates both the difficulties they face and their "joy of betraying Big Brother," as one of the Feminist Five wrote of the defiance she felt during her detention. Tracing the rise of a new feminist consciousness now finding expression through the #MeToo movement, and describing how the Chinese government has suppressed the history of its own feminist struggles, Betraying Big Brother is a story of how the movement against patriarchy could reconfigure China and the world.


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Home Forums > Legacy TRIBE MAGAZINE Music Genre Forums > House Room >
The Pioneers & Innovators of Dance Music
Discussion in 'House Room' started by mondo, Aug 27, 2003.
mondo TRIBE Promoter
On the final day of the conference, Billboard unleashed it's most dynamic panel yet with Step Back in Time: The Pioneers & Innovators of Dance Music. Featuring industry veterans Jocelyn Brown, Nicky Siano, Gloria Gaynor, François K., Tommy Silverman, Mel Cheren, Jellybean Benitez and Nile Rodgers (only Tom Moulton was a no-show), this panel was rich in the history, success and knowledge gained from some of the most important leaders in the field. Moderated by Billboard's own voice of the underground, Dance Tracks writer Michael Paoletta, the standing room only crowd was treated to a unique exchange that featured gossip, innuendo, and conflict - all the things that make New York nightlife what it is! Here are the highlights?!
Nicky Siano on the creative process and the current state of New York nightlife?
Nicky:
I think that what happens in a recording studio when you interact with other people is that there's an energy you share - it's a spiritual kind of energy. You join that energy together and create a project that not only has your energy, but it has the other person's energy [as well].
I just did a remix of an old record of mine called "Tiger Stripes" and I was working on this track, alone, at my house on the computer. Then someone else came in [up-and-comer, Jon Martin] and they added their energy to the project, and it made it better - I allowed that to happen. You know, sometimes we get so caught up in our own ego and pride, that we don't allow other spiritual influences or other elements to come into our realm and to help us. I think that everything can really add to the experience?we should be open to letting the experience unfold rather than control it and make it what you think it should be. Sometimes, the thing you think it should be in your head, is not always the best thing. Keep it all open to the higher plan.
[nicky siano]
The experience I see is that everything has become more club-driven, than DJ-driven. I think that Studio 54 was the first place where that shifted - where it started to become about the club, and since then (well, Garage in the 80's), but what other party has broken through? Body & Soul has broken through. I hope we're making a mark with Twelve West [now defunct], but I think today it's more about the club in a sense. I think how we [can] take back our power, is by joining together - talking to each other. I encourage dialog. There was one thing back then?all my friends were DJs and we talked about what we were playing, where we got our records, how they could get a copy, and that kind of community I don't see existing here. I would love that... I'm very open to that.
Radio vs Clubs for working a record - then and now - the heat rises?
François K: What radio?
Mel Cheren: We were very fortunate in the 70's to have a radio station like WBLS with someone like Frankie Crocker; Mike Wells at KTU; and Barry Mayo at KISS -they understood the power of the clubs. Frankie, [who would come to the Garage] was up in the booth night after night. Frankie came in one Friday night, and he heard Loose Joints, "Is It All Over My Face", -- Monday it was on the radio. Today, you have to have a special dispensation from God and $45 grand. Today, radio is designed by people living in some other state or some foreign country and it just doesn't make any sense?
FK: Yes, it does make sense!
MC: Why?
[Francois Kervokian]
FK: Because advertisers pay for a certain ratio of listeners; they guarantee that they are attracting a certain amount of listeners so?
MC: But Francois?
FK: It's just a business, you should know!
FK: Look, nobody is disagreeing with you, but the problem is that radio in those days was not run like a business. There was still an element of passion and interest left in it. Today it's run like a complete business. It probably will cost you about fifty-five million dollars to purchase an FTC license to broadcast in the city of New York. Then it will cost you an average of 20-30 million dollars a year to run a staff - all these things that it takes to run a radio station are in the way of programming the music you want. You are only going to play the music that your advertisers want you to play.
Tommy: [Radio] really doesn't matter to me?radio will come and go. About two weeks after KTU - 92 KTU - started on the air, and within a month after KTU's first book (ratings report), the format went to #1. About fifty other cities around the country switched over from country to dance music. There was no market place for this and within six months, those stations stopped playing disco and happily declared disco dead. But you know what, by year-end, there were dance records in the American Top Ten. It never changed, it was just the consumer perception. Whether the radio plays dance music or doesn't play dance music, it has nothing to do with the success of dance music. Dance music is the shit! It was always the shit and it will always be the shit! Today, radio has nothing to do with passion.
And then there was some gossip?
[Michael Paoletta, Mel Cheren, Jelly Bean Benitez & Nile Rodgers]
Michael: Nile Rodgers, a secret story about Diana Ross?
Nile: Uhhhhh?
Nicky: I have a Diana Ross story? at Studio 54, the record bins were built into the counter and Diana loved to sit on the records and overlook the crowd like the diva that she was. One night Ritchie Hazar was playing and umm?maybe I shouldn't tell this story...
Crowd yells and begs for more
Nicky continues... So Ritchie moved her forward to the dance floor which was about 30 feet below because he didn't want her to be sitting on his records. That was the end of that!
Nile: I have a good Frankie [Crocker, now deceased] story, too. The good thing about working back in the day, at least for me, is we really chose our own destiny. Bernard [Edwards] and I, we picked the singles for the artist and the label, and we had to come up with the whole promotional campaign. You know, we came up with all the ideas and stuff so we knew that Diana's [Ross] first record was going to be called "Upside Down." And we also knew that second record would be, "I'm Coming Out". So Diana went off to dinner with Frankie, and she said "I'm working with these new boys from New York City and they wrote this song for me and I think it's really good." So Frankie listened to it and Diana came back into the studio, completely in tears and said that Frankie told her that Bernard and I had single-handedly, ruined her career. The thing that was funny about it, is that up until that moment, we really had bonded, you know what I mean? I still looked upon her as like, royalty. And the thing that was really funny, was all that I needed to console her was a drive in my car? I had this wild Porshe with like sub-woofers and stuff. So we got in my car, took off the top and went out to White Castles in Queens.
We were in the parking lot of White Castles, pumping that song and people were coming around the car because it was new. We had just done ["I'm Coming Out"], and this was the rough mix. People were coming around the car and they were dancing and I said, ' Diana, this is how I figure out whether a record is a hit or not.' You give it to a DJ, they play it and in the old days it was just like this -- either the people danced or they didn't. Either you packed the floor or you cleared it. And that was it. We went out to White Castles and we packed the floor. Anyway, that was my story.
Gloria Gaynor on "I Will Survive"?
Michael Paoletta: For Gloria Gaynor, when you recorded, "I Will Survive", it was originally a B-Side, is that correct?
Gloria Gaynor: Yes it was.
MP: When did DJs start playing it?
Nicky: Ritchie Kazar was the first.
MP: Why don't you tell that story.
GG: Well, it was originally for the B-side and when we read the lyrics, my husband/ manager and I, we thought, 'You're gonna do what and put this where?' Because we could read the lyrics and see that it was a timely tune. Anyone who heard the song would know that it was going to be a hit. The record company did not want to know; it was not something that they wanted. So I said we were going to do a show and let the audience decide. Let's take it to Ritchie?so we took it to Ritchie Kazar at Studio 54 where he played it and the audience immediately loved it. It filled up the dance floor. Ritchie was the one who played it, turned it on to all his friends -his DJ friends which is why we took it to him in the first place. We knew that he was influential and he knew what to do with this kind of record. And uh, the rest is history.
Jocelyn Brown on "Push, Push in the Bush"?
Michael: Jocelyn, when you were in the studio recording the Musique song, "Push, Push in the Bush", what was going on in your mind?
(Everyone laughs!)
Jocelyn Brown: I have to say something about this because this is a really important situation here? ladies having an opportunity to sing certain words that might mean something entirely different towards another person's ear, [but it's] not the way the words are interpreted from the lyrics themselves. Sometimes we get kind of stuck because we say certain things such as, "Ummm" or "She is so wrong". But it's not a situation about being wrong, it's about the situation of the lyrics of the song being that particular phrase. It's not that we are trying to be fresh or nasty, or unlady-like, but it's just that sometimes it causes us to do a holler, a scream, a screech or maybe a real long note to make something happen that's effective for that particular word. "Push, Push in the Bush" blew up when the singer said (singing), "You know we got to get down!" That was it - that was dope! So, don't take everything for the worse.
From the legends, their most legendary songs?
Michael: For everybody up here, what song has most turned your life around? Starting with Nicki?
NS: Love is the Message. David Rodriguez and I were sitting in Dawn's office at Columbia and she said, "I only have one copy of this." So I said, 'You only have one copy of this?', and David starts looking at me because there's a copy on the floor. You know, it was dark in there but we were DJs - we could see in the dark! Well, we walked out with two copies of that record.
JB: Patty Labelle came by with a song, it was during a crisis time - her sister's death - a song called, "If Only You Knew". That song stood out for me and still rings in my heart.
GG: Well if I say, "I Will Survive" everyone's going to laugh?but it certainly has done so much for me. It's taken me to more than eighty countries; it's gotten me some nice fat checks - bought me plenty of shoes. Basically, what "I Will Survive" has done for me is it's broadened my scope because nothing broadens your scope like travel, and no song has taken me further in the world than "I Will Survive."
FK: Voodoo Chile by Jimi Hendrix. If I hadn't heard that song I would probably be doing biochemical engineering for a company.
[Francois Kevorkian and Tommy Silverman]
TS: I was trying to think of one because there are so many for me?but I think the one record or album that's really the most important for me is Dr Buzzard's Original Savannah Band. Whenever I hear that, I close my eyes and I am right back at the Garage. Another all-time favorite, "What's Going On" by Marvin Gaye or "Native New Yorker" [by Odyssey]? "There But for the Grace of God"?
[Jelly Bean and Nile Rodgers]
JB: My main one is "Love is the Message," the next is "Power" by Earth, Wind and Fire, "City, Country, City" by War.
[NileRodgers]
NR: When I narrow it down, one of the key records for me was a song that we wrote for ourselves, "Good Times." That record changed everything in my life on so many levels because it was, for all intents and purposes, the beginning of hip-hop and any records that would have long breakdowns, everybody was doing their thing to it. We would go out to these different clubs in the Bronx and Queens and in particular, one called Leviticus. We walked in there [one night] and the DJ was playing this record and I paused - cause you got to remember back in those days DJs used to take liberties and if you had a nice breakdown on your record, they would start rapping and doing all sorts of things over it in the booth. I heard this beat that sounded like my record, but it was different. I thought it was the DJ doing it and then he told me he bought it up on 125th Street and I said, 'You did what?!' What it showed me was that, your music can touch someone else and they use it to create something else. People, for the first time in my world, started playing with my stuff and that was very weird for me - I didn't know how to take it.
But the other thing that I have to tell you that was unbelievable for me, was when we wrote "We Are Family" for Sister Sledge - it really taught me something about my life and something about the power of the groove. When we wrote that, they had never heard the demo - they heard it in the studio for the first time. And Jocelyn will tell you, when you hear them doing that party talk and ad-libbing, that's really what they were doing when they first heard the song - when we were first getting to know each other. I was like 'Oh, My God!' You got to understand that this whole dance thing, this whole disco thing was starting to unravel in front of our faces and even though we thought we knew what we were doing, believe it or not, we were just experimenting. But I had to try and pretend like I had it all planned? that I knew what I was doing when we were really just finding out things as we went along. [But it was] that whole act of discovery, that whole process of sharing in other people's lives that was unbelievable to me. [undaground archives]
mondo, Aug 27, 2003
luvslife TRIBE Member
Wow. That's really cool.
Really interesting to hear them talking about Diana Ross and Club 54 like I would talk about hanging with my buddies.
luvslife, Aug 27, 2003
Bloom! Productions TRIBE Member
it's so important to know our ROOTS.
deeno
Bloom! Productions, Aug 28, 2003


Sometimes in life we have to look long term. But more often than not we don't. One great piece of stress comes from trying to cross bridges before we get to them.
You never know how your course may change and if that bridge will even still be on your path when the time comes or if you'll have to cross an entirely different bridge.
So remember to enjoy where you are, and enjoy the journey, and don't worry about crossing a bridge until you have to set foot onto it.


text:
Latest research shows 58% of Council's support self and custom build.…
HOMEsteven@tectamers.co.uk2017-12-14T17:40:00+00:00
LEAPER LAND PROMOTION
CREATING VIBRANCY AND VALUE IN RURAL COMMUNITIES
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We believe that sensitive development in sustainable and deliverable locations can be achieved with the right approach and through community engagement. The low levels of new housing in rural areas over the last thirty years has threatened the very existence of many villages across the country. We believe that new small-scale housing developments will attract and retain young and growing families who have an important role to play in enhancing and maintaining the vitality and vibrancy of their villages and their communities.
We focus on smaller parcels of land that tend to be overlooked by the traditional land promoter and will consider sites ranging from a single acre upwards in areas where we believe there is an opportunity for sensitively designed new housing that takes into consideration the needs of the whole community.
We work with landowners to help them engage with the local community and will steer them through all the stages of planning through to sale. By taking away the burden of cost as well as many of the time commitments inherent in the process, we make it possible for landowners to effectively understand and address the important concerns that are raised by local residents when new developments are proposed.
We firmly believe that by providing the right access to information throughout the process and by applying a hands-on approach to working with the local community, that we can deliver sensitively designed schemes that are to the benefit of all involved.
Key to our success is building relationships with all stakeholders throughout the process. We look to engage with everyone involved, from local residents through to the planning authority.
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© Copyright | Leaper Land Promotion Ltd | Registered in England, Company No: 10643972
VAT No: 81345701 | Norfolk Website Design by Tec Tamers LLP View our Privacy & Cookie Policy
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text:
import { JwtHelperService } from '@auth0/angular-jwt';
import {Injectable} from "@angular/core";
import {HttpClient} from "@angular/common/http";

@Injectable()

export class AuthService {

	private token : string = localStorage.getItem("jwt-token");

	constructor(
		private jwtHelperService: JwtHelperService,
		private http: HttpClient) {}

		//token : string = this.jwtHelperService.tokenGetter();
		public isAuthenticated(): boolean {
			const token = localStorage.getItem('jwt-token');
			// Check whether the token is expired and return
			// true or false
			return !this.jwtHelperService.isTokenExpired(token);
		}

	//token : string = this.jwtHelperService.tokenGetter();
	// loggedIn() {
	//
	// 	if (this.token) {
	// 		return false;
	// 	}
	//
	// 	const tokenExpired: boolean = this.jwtHelperService.isTokenExpired(this.token);
	//
	// 	return !tokenExpired
	// }

	// decodeJwt() : any {
	// 	let isLoggedIn : boolean = this.loggedIn();
	//
	// 	if (!isLoggedIn) {
	// 		return false;
	// 	}
	// 	const authObject = this.jwtHelperService.decodeToken(this.token);
	//
	// 	return authObject;
	// }

}

redpajama_set_name: RedPajamaGithub


text:
HS 250h News
Slow-selling Lexus HS 250h already getting the axe?
Zach Bowman
Nov 14th 2011 at 11:29AM
Lexus may stop production of the HS 250h. Reports have emerged that the model is suffering from flagging sales and that the luxury automaker may seek to replace the vehicle with a less-expensive, more youth-oriented product in the near future. Last month, Lexus managed to sell just 250 HS 250h units, which is a decline of 72.8 percent compared to the same (already low) period last year. Originally envisioned as a more upscale version of the Toyota Prius, the awkwardly styled HS 250h carries a substantial price tag that has likely done much to scare off would-be buyers. At over $37,000, the vehicle hasn't done a good job of convincing consumers of its merits. The modelhas only been on sale since late 2009 as a 2010 model, so if the reports are true, the HS 250h would lead a very brief life.
Should Lexus decide to kick the hybrid four-door off the team, the company will likely replace it with something more accessible for buyers. Reports suggest that the newcomer will likely cost somewhere around $30,000 and follow a marketing path similar to what's seen with the current CT 200h hatchback, a model that's been much more successful. That sounds nice, but we have to wonder if Lexus really needs two compact hybrids in the same price range.
Featured GalleryReview: 2010 Lexus HS 250h
Lexus HS 250h Information
More HS 250h Information
News Source: Ward's Auto - sub. req. via LeftLaneNews
Image Credit: Copyright 2011 Drew Phillips / AOL
2012 Lexus HS 250h


The V40 first hit the British market in 1996 alongside the S40 saloon. V40s were built in Holland rather than Sweden. At launch, it was only available with 1.8 and 2.0-litre petrol engines with a 1.9 turbo diesel being added later in the year. In early 2004 the V40 began to be phased out in favour of the V50. However, an all-new V40 was launched in 2012. Newer models are sleek and stylish, offering up-market looks.
The V40 is pretty much a "lifestyle" car, so don't expect it to be able to carry huge loads. Boasting a wide range of safety features, you can count on this car to be a reliable buy. It was one of the first cars to feature a pop-up bonnet, while there are plenty of airbags on the inside to keep all passengers safe. It comes with either a standard or sports suspension and the interior is spacious, meaning the ride is comfortable.
A used V40 is practical, safe, well equipped and quite roomy. The handling is satisfactory and the petrol turbo versions are surprisingly rapid. Suspension improvements from 2000 onwards means that later cars ride and handle better than early ones. As you'd expect of any used Volvo, the V40 is packed with safety features, including multiple airbags and Side Impact Protection (SIPS). It's practical and well equipped, making for a sound choice.
Got a specific Volvo V40 model in mind?


text:
Biden outpacing Trump, Obama with diverse judicial nominees
By SEUNG MIN KIM and COLLEEN LONG - Associated Press
Susan Walsh - staff, AP
FILE - President Joe Biden and Supreme Court nominee Judge Ketanji Brown Jackson watch as the senate votes on her confirmation from the Roosevelt Room of the White House in Washington, April 7, 2022.
Alex Brandon - staff, AP
FILE - Supreme Court nominee Ketanji Brown Jackson testifies during her Senate Judiciary Committee confirmation hearing on Capitol Hill in Washington, March 23, 2022.
Tom Williams - pool, Pool CQ Roll Call
FILE - Regina Rodriguez, nominated to be a U.S. district judge for the District of Colorado, speaks during a Senate Judiciary Committee hearing on pending judicial nominations, April 28, 2021, on Capitol Hill in Washington.
FILE - Candace Jackson-Akiwumi, nominee to be U.S. Circuit Judge for the Seventh Circuit, testifies before a Senate Judiciary Committee hearing on pending judicial nominations on Capitol Hill in Washington, April 28, 2021.
Amanda Andrade-Rhoades - freelancer, FR171810 AP
FILE - Florence Y. Pan, a nominee to be a United States District Judge for the District of Columbia, speaks to judicial nominees during a Senate Judiciary Hearing on Capitol Hill in Washington on July 14, 2021.
FILE - Myrna Perez, of New York, a nominee to be United States Circuit Judge for the Second Circuit, testifies before the Senate Judiciary Committee during a hearing on Capitol Hill in Washington, July 14, 2021.
Manuel Balce Ceneta - staff, AP
FILE - Nominee Kea Whetzal Riggs to be U.S. District Judge for the District of New Mexico, testifies during a Senate Judiciary Committee nominations hearing on Capitol Hill in Washington, June 26, 2019.
FILE - From left, nominees Douglas Russell Cole and Matthew Walden McFarland to be U.S. District Judges for the Southern District of Ohio; Robert Anthony Molloy to be District Court of the Virgin Islands Judge; and Kea Whetzal Riggs to be U.S. District Judge for the District of New Mexico are sworn in during a Senate Judiciary Committee nominations hearing on Capitol Hill in Washington, June 26, 2019.
Mariam Zuhaib - staff, AP
FILE - Jeffery Paul Hopkins speaks during a Senate Judiciary Committee oversight nomination hearing to be U.S. District Judge for the Southern District of Ohio, Oct. 12, 2022, on Capitol Hill in Washington.
Kevin Lamarque - pool, Pool Reuters
FILE - Julien Neals, nominated to be U.S. District Judge for the District of New Jersey, listens during a Senate Judiciary Committee hearing on pending judicial nominations, April 28, 2021 on Capitol Hill in Washington.
FILE - Zahid Quraishi, nominated by U.S. President Joe Biden to be a U.S. District Judge for the District of New Jersey, speaks during a Senate Judiciary Committee hearing on pending judicial nominations, Wednesday, April 28, 2021, on Capitol Hill in Washington.
FILE - Nominee Robert Anthony Molloy to be District Court of the Virgin Islands Judge, testifies during a Senate Judiciary Committee nominations hearing on Capitol Hill in Washington, June 26, 2019.
FILE - Nominee Douglas Russell Cole to be U.S. District Judge for the Southern District of Ohio, testifies during a Senate Judiciary Committee nominations hearing on Capitol Hill in Washington, June 26, 2019.
FILE - Nominee Matthew Walden McFarland to be U.S. District Judge for the Southern District of Ohio, testifies during a Senate Judiciary Committee nominations hearing on Capitol Hill in Washington, June 26, 2019.
WASHINGTON (AP) — For the Biden White House, a quartet of four female judges in Colorado encapsulates its mission when it comes to the federal judiciary.
Charlotte Sweeney is the first openly LGBT woman to serve on the federal bench west of the Mississippi River and has a background in workers' rights. Nina Wang, an immigrant from Taiwan, is the first magistrate judge in the state to be elevated to a federal district seat.
Regina Rodriguez, who is Latina and Asian American, served in a U.S. attorney's office. Veronica Rossman, who came from the former Soviet Union with her family as refugees, is the first former federal public defender to be a judge on the 10th U.S. Circuit Court of Appeals.
With these four women, who were confirmed during the first two years of President Joe Biden's term, there is a breadth of personal and professional diversity that the White House and Democratic senators have promoted in their push to transform the judiciary.
"The nominations send a powerful message to the legal community that this kind of public service is open to a lot of people it wasn't open to before," Ron Klain, the White House chief of staff, told The Associated Press. "What it says to the public at large is that if you wind up in federal court for whatever reason, you're much more likely to have a judge who understands where you came from, who you are, and what you've been through."
Klain said that "having a more diverse federal bench in every single respect shows more respect for the American people."
The White House and Democratic senators are closing out the first two years of Biden's presidency having installed more federal judges than did Biden's two immediate predecessors. The rapid clip reflects a zeal to offset Donald Trump's legacy of stacking the judiciary with young conservatives who often lacked in racial diversity.
So far, 97 lifetime federal judges have been confirmed under Biden, a figure that outpaces both Trump (85) and Barack Obama (62) at this point in their presidencies, according to data from the White House and the office of Senate Majority Leader Chuck Schumer. D-N.Y. The 97 from the Biden presidency includes Supreme Court Justice Ketanji Brown Jackson, that court's first Black woman, as well as 28 circuit court judges and 68 district court judges.
Three out of every four judges tapped by Biden and confirmed by the Senate in the past two years were women. About two-thirds were people of color. The Biden list includes 11 Black women to the powerful circuit courts, more than those installed under all previous presidents combined. There were also 11 former public defenders named to the circuit courts, also more than all of Biden's predecessors combined.
"It's a story of writing a new chapter for the federal judiciary, with truly extraordinary folks representing the broadest possible types of diversity," said Paige Herwig, a senior White House counsel.
The White House prioritized judicial nominations from the start, with Biden transition officials soliciting names of potential picks from Democratic senators in late 2020. Sen. Dick Durbin, D-Ill., chairman of the Senate Judiciary Committee, swiftly moved nominees through hearings and Schumer set aside floor time for votes.
Particular focus was placed on nominees for the appellate courts, where the vast majority of federal cases end, and those coming from states with two Democratic senators, who could find easier consensus in a process where there's still significant deference given to home-state officials.
Democrats hope to speed up the tempo of confirmations next year, a goal more easily accomplished by a 51-49 Senate that will give them a slim majority on committees. In the past two years, votes on some of Biden's more contested judicial nominees would deadlock in committee votes, requiring more procedural steps that ate up valuable Senate floor time.
Schumer said he also hopes to install more judges in appeals courts that shifted rightward under Trump, an effort that the majority leader described as rebalancing those courts.
"Trump loaded up the bench with hard right 'MAGA' type judges who are not only out of step with the American people, they were even out of step with the Republican Party," Schumer said in an interview, using shorthand for Trump's 2016 campaign slogan, "Make America Great Again."
Schumer added: "We had a mission, it's not just a predilection. It was a mission to try and redress that balance."
Despite their limited power to actually derail Biden's judicial picks, some Republicans have fought ferociously against many of them, arguing that their views were out of the legal mainstream despite Democratic arguments otherwise. The precarious 50-50 Senate, where Schumer's plans were often thwarted by ailments or absences, meant several Biden nominees languished for months and were never confirmed before the Senate wrapped up its work this year.
Democrats also say certain judicial nominees, particularly women of color, were unfairly targeted by their GOP critics, leading to tense fights in the Judiciary Committee.
"The Republicans have just got a problem with this. Not all of them, some do," Durbin said in an interview. "And when you call them out on it … 'Why is it consistently women of color that are the object of your wrath?' and they can't answer."
Sen. Josh Hawley, R-Mo., a committee member, said Biden's picks were "very, very left, but unapologetically so." He said Durbin's assertions about Republicans were "absurd."
"I think the president made a commitment to his base that he was going to put people who shared a very left-wing worldview, who are generally quite critical of, for instance, the criminal justice system, think that it is systemically racist," Hawley said.
Despite the strengthened Democratic majority, the White House could nonetheless confront some challenges when it comes to nominating and confirming judges over the next two years.
For instance, Biden has made barely a dent in the number of vacancies for district court judges in states that have two Republican senators, confirming just one such person: Stephen Locher, now a judge in the Southern District of Iowa. Senators still adhere to a practice that allows home-state senators virtual veto power over district court picks — a process known colloquially as the "blue slip" — and Democrats are facing an increased push from advocates to discard the tradition, arguing that it only allows for Republican obstructionism.
For instance, Republican Sen. Ron Johnson of Wisconsin earlier this year blocked action on William Pocan, nominated to serve in the Eastern District of Wisconsin, after initially recommending him as part of a bloc of nominees to the White House. Durbin has said he would reconsider the current "blue slip" practice if he sees systematic abuse by senators, especially based on a nominee's race, gender or sexual orientation.
But cases like Pocan's have been rare, Durbin said, and other influential Republicans are affording some level of deference to the Biden White House when it comes to judges.
"I can't think of a system where Republicans get all their judges and Democrats get none of theirs," said South Carolina Sen. Lindsey Graham, who will be the top Republican on the Judiciary Committee next year. "That's not a viable system."
One matter Biden has not been willing to address: the structure of the Supreme Court.
Any push to change the highest court in the land, even in small ways, has found little footing at the White House, with Biden aides instead highlighting the president's push to nominate federal judges as the best and most substantial way to secure a Democratic legacy in the judiciary.
As Biden took office in 2021, calls for changes to the Supreme Court were growing louder, after Trump named three new justices that tilted the court's makeup far to the right.
In June, the 6-3 conservative majority overturned the landmark decision Roe v. Wade, eliminating the constitutional protections for abortion that had existed for nearly 50 years. It did so despite a majority of people in the United States believing abortion should be legal. In the same term, the justices also weakened gun control and curbed the Environmental Protection Agency's ability to manage climate change.
Polls have shown a dip in approval for the court and respect for it. A Gallup Poll found Americans had the lowest level of trust in the court in 50 years.
Biden has spoken out about the rulings, and argued the court is more of an "advocacy group these days." But he has not embraced calls to expand the court or even to subject justices to a code of conduct that binds other federal judges. He has not spoken publicly about a study he commissioned on the future of the Supreme Court that finished last year and suggested term limits, mandatory retirement and judicial ethics codes as ways to restore trust in the institution.
White House officials similarly have declined to weigh in on potential changes, even as those advocating for change believe the push will grow stronger this term, as voting rights, clean water, immigration and student loan forgiveness come before the justices.
"I wouldn't, in any way minimize the progress and the importance of what President Biden is doing on the lower courts," said Chris Kang of Demand Justice, an advocacy group leading the push to expand the court. "But at the same time, we need to look at the core problem, which is the Supreme Court, and what can be done to fix the issues."
For now, the White House's focus will remain on the people who sit on the courts.
It's a particularly meaningful achievement for Biden, a former Judiciary Committee chairman himself, and for Klain, who was chief counsel for Biden on that committee and a lawyer who worked on judicial nominations in the Clinton White House.
"With all due respect to my predecessors, I'm sure this is a higher priority for me," said Klain, who meets weekly with the judicial nominations team. But, referring to Biden, Klain added: "The fact that he makes it such a priority, makes it a big priority for me."