text:
\section{Introduction}

Pair production in an external field is a form of semiclassical tunneling
and has applications in many areas of physics~\cite{Parker:1969au,Zeldovich:1971mw,Hawking:1974rv,Casher:1978wy,Ringwald:2001cp,Kharzeev:2005iz}.
Here we present a complete first-principles calculation of the one-loop
thermal correction to the pair production rate of charged scalars
in a static electric field. The effect of pair production in a background
electric field at zero temperatue was derived first by Euler and Heisenberg~\cite{Heisenberg:1935qt}
and subsequently rederived by Schwinger~\cite{Schwinger:1951nm}
using modern field-theoretic techniques.
the pair production is simple: when the energy contained in an external
electric field is large enough, it becomes energetically favorable
to produce charged pairs which screen the external field. From a modern
perspective, the presence of an external electric field over a large
spatial region creates a metastable state, which decays by the nucleation
of charged-particle pairs. In this way, it is similar to the false
vacuum decay~\cite{Langer:1967ax,Coleman:1977py,Callan:1977pt}.
This similarity is most clearly seen in the worldline formalism, as
shown in the calculation of the zero-temperature pair production rate
by Affleck \emph{et al.}~\cite{Affleck:1981bma}. The inclusion of
thermal effects naturally increases the rate at which the metastable
state decays~\cite{Affleck:1980ac}.

Schwinger's expression for the decay rate is obtained from the imaginary
part of the one-loop effective action of charged particles in a constant
external electric field. For charged scalars, the one-loop zero-temperature
decay rate is
\begin{equation}
\Gamma=\frac{\left(eE\right)^{2}}{\left(2\pi\right)^{3}}\sum_{p=1}^{\infty}\frac{\left(-1\right)^{p+1}}{p^{2}}\exp\left[-\frac{m^{2}}{eE}\pi p\right]\label{eq:Schwinger-scalar-rate}
\end{equation}
with a similar result for fermions. The factor of $1/e$ in the exponent
signals that this is a nonperturbative result. These results have
been extended in a number of ways~\cite{Brezin:1970xf,Popov:1973az,Marinov:1977gq,Dunne:2004nc,Gies:2005bz,Dunne:2005sx,Dunne:2006st,Dunne:2012vv}.
One obvious extension is to to nonzero temperature and density. In
the case of external \emph{magnetic} fields, the properties of the
thermal one-loop effective action are well-known~\cite{Dittrich:1979ux,Elmfors:1993wj}.
However, in the case of electric fields, there has been no clear consensus
on the form or even the existence of one-loop thermal corrections
to the zero-temperature decay rate~\cite{Loewe:1991mn,Elmfors:1994fw,Hallin:1994ad,Ganguly:1995mi,Ganguly:1998ys,Gies:1998vt,Gies:1999vb}.
Although the formal expression for the decay rate can be readily constructed
using, say, Schwinger's proper time formulation, the analytic structure
of the resulting formulae is quite intricate and leads to structural
ambiguities~\cite{Gies:1998vt}. It has been suggested that the one-loop
thermal contribution to the decay rate may be zero, but there is no
obvious symmetry principle that would lead to this conclusion. The
worldline formalism has proven to be a very powerful tool in quantum
field theory at zero temperature, capable of reproducing and extending
Schwinger's result~\cite{Affleck:1981bma,Dunne:2005sx,Dunne:2006st}
as well as providing a compact, powerful framework for the calculation
of gauge theory amplitudes~\cite{Bern:1991aq,Strassler:1992zr} We
will show that the worldine formalism can be used to calculate the
thermal corrections to Schwinger's one-loop result. To the best of
our knowledge, this is the first time the worldline formalism has
been used to calculate a nonperturbative finite-temperature effect.
We restrict ourselves here to the simplest case of charged scalars in
QED, and will return to the case of fermions in QED and QCD in later
work. The extension of the worldline formalism to fermions presents
no difficulty~\cite{Schubert:2001he,Dunne:2005sx}. The case of QCD
is relevant, for instance, in phenomenological flux-tube models of
quark-antiquark pair production during hadronization in heavy ion
collisions~\cite{Casher:1978wy,Andersson:1983ia,Bass:1998ca}.

\section{The $T=0$ case in the worldline formalism}

We begin by reviewing and extending the work of Affleck \emph{et al.}~\cite{Affleck:1981bma}
for the $T=0$ case of a scalar field. The Lagrangian is given by
\begin{equation}
\mathcal{L}=\left(D_{\mu}\phi\right)^{*}\left(D_{\mu}\phi\right)+m^{2}\phi^{*}\phi
\end{equation}
with a covariant derivative $D_{\mu}\equiv\partial_{\mu}+ieA_{\mu}$
where $A_{\mu}$ provides the constant background electric field in
Euclidean space. The partition function $Z[A]$ and effective action
$W[A]$ are functionals of the background field:
\begin{equation}
Z\left[A\right]=e^{-W[A]}=\int\left[d\phi\right]\left[d\phi^{*}\right]e^{-\int d^{4}x\mathcal{L}}.
\end{equation}
The integral over the scalar fields can be done exactly, yielding
a functional determinant which can be written as an integral over
proper time:
\begin{equation}
W\left[A\right]=-\int_{0}^{\infty}\frac{ds}{s}\Tr\left[e^{-s\left(-D^{2}+m^{2}\right)}\right]=-\int_{0}^{\infty}\frac{ds}{s}e^{-sm^{2}}\left\langle x\left|e^{-s\left(-D^{2}\right)}\right|x\right\rangle .
\end{equation}
In the worldline formalism, the trace is given as a path integral
over closed worldline paths $x_{\mu}(\tau)$
\begin{equation}
W\left[A\right]=-\int_{0}^{\infty}\frac{ds}{s}e^{-sm^{2}}\oint\left[dx_{\mu}\right]\exp\left\{ -\int_{0}^{s}d\tau\left[\frac{1}{4}\left(\frac{dx_{\mu}}{d\tau}\right)^{2}+ieA_{\mu}\frac{dx_{\mu}}{d\tau}\right]\right\}
\end{equation}
with boundary condition $x_{\mu}\left(0\right)=x_{\mu}\left(s\right)$.
We perform first a saddle point approximation to the integral over
$s$ and then find instanton solutions to the equations for $x_{\mu}(\tau)$.
By rescaling $s$ and $\tau$, we can put $W[A]$ into the form~\cite{Dunne:2005sx}
\begin{equation}
W\left[A\right]=-\int_{0}^{\infty}\frac{ds}{s}e^{-s}\oint\left[dx_{\mu}\right]\exp\left\{ -\int_{0}^{1}du\left[\frac{m^{2}}{4s}\dot{x}^{2}+ieA\cdot\dot{x}\right]\right\}
\end{equation}
where $\dot{x}_{\mu}\equiv dx_{\mu}/du$. The saddle point of the
integral over $s$ is given by
\begin{equation}
s_{0}^{2}=\frac{m^{2}}{4}\int_{0}^{1}du\,\dot{x}^{2}
\end{equation}
and its contribution to $W[A]$ is
\begin{equation}
-\sqrt{\frac{2\pi}{m}}\oint\left[dx_{\mu}\right]\frac{1}{{\textstyle \left[\int_{0}^{1}du\,\dot{x}^{2}\right]^{1/4}}}\exp\left[-m\sqrt{\int_{0}^{1}du\,\dot{x}^{2}}-ie\int_{0}^{1}du\,A\cdot\dot{x}\right].
\end{equation}
This will be a good approximation if $s_{0}\gg1$, corresponding to
$eE/m^{2}\ll1$~\cite{Dunne:2005sx}. We may now evaluate the functional
integral in steepest descents, thus reducing the problem to finding
instanton solutions for the effective action
\begin{equation}
S_{\mathit{eff}}=m\sqrt{\int_{0}^{1}du\,\dot{x}^{2}}+ie\int_{0}^{1}du\,A\left(x(u)\right)\cdot\dot{x}.\label{eq:eqm}
\end{equation}
This entails solving the following equations of motion:

\[
\frac{1}{\sqrt{\int_{0}^{1}du\,\dot{x}^{2}}}m\dot{x}_{\mu}=ieF_{\mu\nu}\dot{x}_{\nu}.
\]
Notice that $\sqrt{\int_{0}^{1}du\,\dot{x}^{2}}$ is a constant of
the motion, as can be verified by contracting the above with $\dot{x}_{\mu}.$

We impose a constant (Minkowski-space) electric field by taking $A_{3}=-iEx_{4}$
with the other three components either zero or constant. Then the
only non-zero components of $F$ are $F_{34}=-F_{43}=+iE$. The general
solution of the equations of motion~\eqref{eq:eqm} for $x_{\mu}\left(\tau\right)$
is a circular orbit of radius $R=m/eE$ centered about $(\bar{x}_{3},\bar{x}_{4})$
\begin{align}
x_{3} & =\frac{m}{eE}\cos\left(\frac{eaE}{m}u+\varphi\right)+\bar{x}_{3}\\
x_{4} & =\frac{m}{eE}\sin\left(\frac{eaE}{m}u+\varphi\right)+\bar{x}_{4}
\end{align}
where the parameter $a=\sqrt{\int_{0}^{1}du\,\dot{x}^{2}}$. In the
case of constant field this equals the arc length, which for $T=0$
is $2\pi pR$, with $p$ a positive integer. The value of the effective
action for such a solution is

\begin{equation}
S_{0p}=\frac{m^{2}}{eE}\pi p.
\end{equation}
The case $p=1$ was treated by Affleck et al., who showed that the
$p=1$ solution has one unstable mode. Their results may be extended
to general $p$ with one caveat: for $p>1$, there is an unstable
mode as in the $p=1$ case, but also $p-1$ extra pairs of negative
eigenvalues. Extra negative modes have been found previously in the
study of vacuum decay, with subtle interpretational issues~\cite{Coleman:1987rm,Liang:1994xn,Battarra:2012vu}.
In the present case, we have guidance from Schwinger's original treatment,
and this tells us that the pairs of negative eigenvalues are included,
with the minus signs cancelling. See Appendix \ref{sec:prefactors}
for a derivation of the fluctuation prefactors $K_{0p}$ associated with these trajectories.
 The final result takes the form
\begin{equation}\label{eq:Schwinger-scalar-rate-demo}
\Gamma_{0}=2\Im\left\{ \sum_{p=1}^{\infty}K_{0p}e^{-S_{0p}}\right\}
\end{equation}
with
\begin{equation}
K_{0p}=\frac{i}{2}\frac{\left(eE\right)^{2}}{\left(2\pi\right)^{3}p^{2}}\left(-1\right)^{p+1}
\end{equation}
reproducing the known result Eq. \eqref{eq:Schwinger-scalar-rate}.

\section{The $T>0$ case in the worldline formalism}

In the worldline formalism, nonzero temperature may be introduced
via the replacement~\cite{McKeon:1992if,Shovkovy:1998xw}
\begin{equation}
\left\langle x\left|e^{-s\left(-D^{2}\right)}\right|x\right\rangle \rightarrow\sum_{n\in Z}\left\langle x\left|e^{-s\left(-D^{2}\right)}\right|x+n\beta\hat{e}_{4}\right\rangle
\end{equation}
in the functional determinant. Finite temperature worldline instantons
are sections of the $T=0$ solutions whose endpoints are separated
by $n\beta$ in the time direction.

For any value of $n\beta$ for which solutions
exist, there is a short path of central angle less than $\pi$ corresponding to a particle trajectory
and another corresponding to an antiparticle trajectory; both trajectories
contribute to the free energy of the metastable phase. Correspondingly,
there are are also two long paths of central angle greater than $\pi$ which contribute to the decay rate.
All four paths are shown in Fig.~\ref{fig:paths}.
From the geometry
we see that the arc length of a short path $R\theta_{n}$ is determined by $R\sin\left(\theta_{n}/2\right)=n\beta/2$.
The arc length of a corresponding long path is $R\left(2\pi-\theta_{n}\right)$.
Appending a short
path of arc length $R\theta_{n}$ to a corresponding long path of
arc length $R\left(2\pi-\theta_{n}\right)$ gives the $T=0$ circular
solution found in Ref.~\cite{Affleck:1981bma}.

\begin{figure}[h]
\centering\input{paths.tex} \caption{\label{fig:paths}The four basic finite-temperature classical paths
in the $x_{3}-x_{4}$ plane with a winding of $\pm n$ in the timelike
direction, shown as portions of zero-temperature circular paths. All
four paths begin and end on the same two points, which are separated
by $n\beta$ in Euclidean time. From left to right, the paths are
an antiparticle long path, an antiparticle short path, a particle
short path and a particle long path. The radius $R$ is $m/eE$ and
the length of the short arcs $a_{n}$ is $R\theta_{n}$. }
\end{figure}

In order for such solutions to exist at all, the diameter of the $T=0$
solution must be greater than $n\beta$,
\begin{equation}
2R=\frac{2m}{eE}>n\beta.
\end{equation}
In other words, the maximum value of $n$, $n_{max}$ is given by
\begin{equation}
n_{max}=\left\lfloor \frac{2mT}{eE}\right\rfloor .\label{eq:nmax}
\end{equation}
This implies that there are no one-loop thermal effects from worldline
instantons for $T<eE/2m$, \emph{i.e.}, at sufficiently low temperatures~\cite{Gies:1999vb}.

Such solutions can be extended by adding on $p$ windings. The actions
of these solutions are given by
\begin{align}
S_{np}^{\left(s\right)} & =\frac{m^{2}}{2eE}\left[\left(\theta_{n}+2\pi p\right)+\sin\theta_{n}\right]\\
S_{np}^{\left(l\right)} & =\frac{m^{2}}{2eE}\left[\left(2\pi-\theta_{n}+2\pi p\right)-\sin\theta_{n}\right].
\end{align}
Note that
\begin{align}
S_{np}^{\left(s\right)} & =S_{n0}^{\left(s\right)}+S_{0p}\\
S_{np}^{\left(l\right)} & =S_{n0}^{\left(l\right)}+S_{0p}
\end{align}
and that the two solutions become degenerate when $\theta_{n}=\pi.$

\subsection{Fluctuation prefactors}

The prefactors $K_{np}^{(s)}$ and $K_{np}^{(l)}$ are
given in terms of the functional determinant of the second variation
operator, which is the sum of a local and a nonlocal term~\cite{Affleck:1981bma}:
\begin{equation}
M_{\mu\nu}\equiv\left.\frac{\delta S_{\mathit{eff}}}{\delta x_{\nu}\left(u'\right)\delta x_{\mu}\left(u\right)}\right|_{x_{\mathit{cl}}}\!=L_{\mu\nu}-\vartheta\frac{eE}{R^{2}}\left(x_{\mu}\left(u\right)-\bar{x}_{\mu}\right)\left(x_{\nu}\left(u'\right)-\bar{x}_{\nu}\right)
\end{equation}
where
\begin{equation}
L_{\mu\nu}=\left[-\frac{eE}{\vartheta}\delta_{\mu\nu}\frac{d^{2}}{du^{2}}+ieF_{\mu\nu}\frac{d}{du}\right]\delta\left(u-u'\right)\label{eq:localpart}
\end{equation}
and $\vartheta$ is the total angle spanned by the instanton solution,
that is, $\vartheta=2\pi p+\theta_{n}$ for short paths and $\vartheta=2\pi\left(p+1\right)-\theta_{n}$
for long paths.
For fluctuations about zero temperature solutions, the
eigenvalue problem for $M_{\mu\nu}$ can be solved by inspection. For fluctuations about finite
temperature solutions this is made difficult by the boundary conditions at the endpoints. Fortunately, the functional
determinant may be computed without any explicit knowledge of the spectrum. The matrix
determinant lemma~\cite{Sylvester:1851fu} can be used to isolate the effect
of the nonlocal term,
\begin{equation}
\det\vphantom{}'\left[M_{\mu\nu}\right]=\det\vphantom{}'\left[L_{\mu\nu}\right]\cdot\left[1-\vartheta\frac{eE}{R^{2}}\iint du\,du'\,\left(x\left(u\right)-\bar{x}\right)_{\mu}\left(L^{-1}\right)_{\mu\nu}\left(x\left(u'\right)-\bar{x}\right)_{\nu}\right]
\end{equation}
and the local part of the functional determinant is computed using the method of Gel'fand and
Yaglom~\cite{Gelfand:1959nq,Levit:1976fv}.
Consider the following set
of initial value problems ($\rho=1,2,3,4$):
\begin{align}
L_{\mu\nu}\eta_{\nu}^{\left(\rho\right)} & =0\\
\eta_{\nu}^{\left(\rho\right)}\left(0\right) & =0\\
\dot{\eta}_{\nu}^{\left(\rho\right)}\left(0\right) & =\delta_{\nu\rho}
\end{align}
Up to a phase, the local prefactor can be written
\begin{equation}
\left(N\det\vphantom{}'\left[L_{\mu\nu}\right]\right)^{-1/2}=
\frac{\left(eE\right)^{2}}{\left(2\pi\vartheta\right)^{2}}\sqrt{\frac{\det\left[\tilde{\eta}_{\mu}^{\left(\nu\right)}\left(1\right)\right]}{\det\left[\eta_{\mu}^{\left(\nu\right)}\left(1\right)\right]}}
\end{equation}
where $N$ is a normalization factor and $\tilde{\eta}_{\mu}^{\left(\nu\right)}$ are the solutions of the corresponding \emph{free} initial value problem,
with $\tilde{L}_{\mu\nu}=-\frac{eE}{\vartheta}\frac{d^{2}}{du^{2}}\delta_{\mu\nu}$.
It is then straightforward to show
\begin{equation}\label{eq:localpre}
\left(N\det\vphantom{}'\left[L_{\mu\nu}\right]\right)^{-1/2}=(-1)^p\frac{\left(eE\right)^{2}}{\left(2\pi\vartheta\right)^{2}}\sqrt{\frac{\vartheta^{2}}{2\left(1-\cos\vartheta\right)}}.
\end{equation}
As we will see in section \ref{sec:topo}, the overall phase $e^{i 2\pi p /2}=(-1)^p$ is related to the Morse index of the classical path. Note that this quantity is manifestly real, which means any imaginary contribution must come from the nonlocal part

To compute the nonlocal part we find the Green's function directly,
by solving the equation
\begin{equation}
L_{\mu\rho}G_{\rho\nu}\left(u-u'\right)=\delta_{\mu\nu}\delta\left(u-u'\right)
\end{equation}
with Dirichlet boundary conditions. A lengthy but straightforward
calculation gives, for the nontrivial components $G_{33} = G_{44}$ and $G_{43} =-G_{34}$,
\begin{align}
G_{33} &=\frac{1}{2eE}\left[-\sin\left(\vartheta|u-u'|\right)+\sin\left(\vartheta u'\right)+
\sin\left(\vartheta u\right)
-\frac{4\sin\left(\frac{\vartheta}{2}u\right)\sin\left(\frac{\vartheta}{2}u'\right)\cos\left(\frac{\vartheta}{2}\left(u-u'\right)\right)}{\tan\left(\frac{\vartheta}{2}\right)}\right]\\
G_{43} &=\frac{1}{2eE}\left[\sgn\left(u-u'\right)\left(\cos\left(\vartheta|u-u'|\right)-1\right)+\cos\left(\vartheta u'\right)-\cos\left(\vartheta u\right)-\frac{\sin\left(\vartheta\left(u-u'\right)\right)+\sin\left(\vartheta u'\right)-\sin\left(\vartheta u\right)}{\tan\left(\frac{\vartheta}{2}\right)}\right].
\end{align}

The nonlocal part of the determinant can now be computed directly:
\begin{equation}
\left[1-\vartheta\frac{eE}{R^{2}}\iint du\,du'\,x_{\mu}\left(u\right)G_{\mu\nu}\left(u-u'\right)x_{\nu}\left(u'\right)\right]=\frac{\vartheta}{2}\cot\left(\frac{\vartheta}{2}\right)
\end{equation}
Note that for long paths $\pi<\vartheta<2\pi$ (modulo $2\pi$), so the nonlocal part of the determinant is negative.
Because of this, it is clear that it is the long paths that contribute to the imaginary
part of the effective action.

The prefactor can now be assembled as before
\begin{align}
\left(\int d^{4}x\right)\frac{\sqrt{2\pi/m}}{\left[\int_{0}^{1}du\,\dot{x}^{2}\right]^{1/4}}\left(\det\vphantom{}'\left[\left.\frac{\delta S_{\mathit{eff}}}{\delta x_{\nu}\left(u'\right)\delta x_{\mu}\left(u\right)}\right|_{x_{\mathit{cl}}}\right]\right)^{-1/2} & =V_{3}\beta\frac{\left(eE\right)^{2}}{\left(2\pi\right)^{3/2}\left(nm\beta\right)^{1/2}\vartheta^{2}}\left[1-\left(\frac{n\beta eE}{2m}\right)^{2}\right]^{-1/4}.
\end{align}
For long paths, an extra factor of $\pm i/2$ should be included
because the contribution to the imaginary part results from an integration over only one half of the Gaussian peak in the imaginary direction~\cite{Coleman:1978ae}.
The sign depends on the way in which the analytic continuation is performed.

The functional determinant for the short paths is always positive,
and the functional determinant for the long paths is always negative,
in agreement with arguments given in section~\ref{sec:topo}.
The sum of the short path contributions represents the free energy
density of the metastable phase, and is given by
\begin{equation}
f=-\sum_{p=0}^{\infty}\sum_{n=1}^{n_{\mathit{\mathit{max}}}}2K_{np}^{\left(s\right)}e^{-S_{np}^{\left(s\right)}}\label{eq:freeenergy}
\end{equation}
where
\begin{align}
K_{np}^{(s)} & =\frac{(-1)^p\left(eE\right)^{2}}{\left(2\pi\right)^{3/2}\left(n\beta m\right)^{1/2}\left[2\pi p+2\sin^{-1}\left(\frac{n\beta eE}{2m}\right)\right]^{2}}\left[1-\left(\frac{n\beta eE}{2m}\right)^{2}\right]^{-1/4}\label{eq:Ksnp}\\
S_{np}^{(s)} & =\frac{m^{2}}{2eE}\left[2\pi p+2\sin^{-1}\left(\frac{n\beta eE}{2m}\right)+\frac{n\beta eE}{m}\sqrt{1-\left(\frac{n\beta eE}{2m}\right)^{2}}\right].\label{eq:Ssnp}
\end{align}
In the limit $E\rightarrow0$, equation \eqref{eq:freeenergy} precisely
reproduces the free energy of a free relativistic particle in the
limit $\beta m\gg1$. Compare the limiting form of equation \eqref{eq:freeenergy} with the exact expression~\cite{Meisinger:2001fi}
\begin{equation}
  f = - \frac{m^2}{\pi^2 \beta^2}\sum_{n=1}^{\infty}\frac{1}{n^2}K_2(n\beta m).
\end{equation}
As $\beta \rightarrow \infty$ we have
\begin{equation}
  f \sim -  \sum_{n=1}^{\infty} 2\frac{m^{3/2}}{(2\pi)^{3/2} (n\beta)^{5/2}}e^{-n\beta m}
\end{equation}
which is the precise form of equation \eqref{eq:freeenergy} as $E\rightarrow 0$.

\begin{figure}
\centering \input{freeenergy.tex} \caption{\label{fig:freeenergy} The worldline instanton expression for the free energy is an excellent approximation at low temperatures and $E\rightarrow0$.}
\end{figure}

The long paths, on the other hand, give a thermal correction $\Gamma_{T}$
to the zero-temperature decay rate $\Gamma_{0}$. Our final result
for scalars is
\begin{equation}
\Gamma_{T}=2\Im\left\{ \sum_{p=0}^{\infty}\sum_{n=1}^{n_{\mathit{\mathit{max}}}}2K_{np}^{\left(l\right)}e^{-S_{np}^{\left(l\right)}}\right\} \label{eq:decayrate}
\end{equation}
where
\begin{align}
K_{np}^{\left(l\right)} & =\frac{i}{2}\cdot\frac{(-1)^p\left(eE\right)^2}{\left(2\pi\right)^{3/2}\left(n\beta m\right)^{1/2}\left[2\pi\left(p+1\right)-2\sin^{-1}\left(\frac{n\beta eE}{2m}\right)\right]^{2}}\left[1-\left(\frac{n\beta eE}{2m}\right)^{2}\right]^{-1/4}\label{eq:Klnp}\\
S_{np}^{(s)} & =\frac{m^{2}}{2eE}\left[2\pi\left(p+1\right)-2\sin^{-1}\left(\frac{n\beta eE}{2m}\right)-\frac{n\beta eE}{m}\sqrt{1-\left(\frac{n\beta eE}{2m}\right)^{2}}\right].\label{eq:Slnp}
\end{align}
This concludes the derivation of our results for scalars in
an external electric field.

\section{Discussion}

In this section, we discuss some of the unusual features of our results,
and their generalization to related problems.
In Fig.~\ref{fig:decayrate} we plot the total decay rate $\Gamma=\Gamma_{0}+\Gamma_{T}$
as a function of $T/m$ for three values of $eE/m^{2}.$ The leftmost
part of each curve represents the contribution of $\Gamma_{0}$ alone,
which is independent of temperature. Each curve shows singularities
at $T/m=neE/2m^{2}$, indicated by dotted lines. Each singularity occurs at a threshold temperature above which a new worldline instanton solution becomes possible.
It can be shown that,
wherever it is nonzero, $\Gamma_{T}$ is always larger than $\Gamma_{0}$.
By examining the reliable values of $\Gamma/m^{4}$ to the left of
each singularity, we see that the overall rise in the decay rate envelope
appears to be linear in $T$.

\begin{figure}[H]
\centering \input{decayrate.tex}

\caption{\label{fig:decayrate}The total one-loop decay rate $\Gamma=\Gamma_{0}+\Gamma_{T}$
divided by $m^{4}$ versus $T/m$ for various values of $eE/m^{2}.$
The dotted lines represent the singularities at $T/m=neE/2m^{2}$,
which are rendered finite by effects not included at one loop. The
leftmost part of each curve represents the contribution of $\Gamma_{0}$
alone. }
\end{figure}

The set of thresholds is controlled by the dimensionless
parameter $2mT/eE$, and by the associated integer part $n_{max}$.
Any finite temperature instanton must satisfy $2R=2m/eE > n\beta$.
If $n_{max}=0$, \emph{i.e.} $T<eE/2m$, there are no finite temperature
instantons, and therefore no
corrections to the zero-temperature decay rate. As $T$ is increased,
the threshold for a new solution is crossed whenever $n_{max}$ increases
by one.
This has some similarity with the problem of vacuum decay at finite temperature.
In the problem of the decay of the false vacuum, the Euclidean bounce
solution in the thin wall approximation is a critical bubble of radius
$R_{c}$, obtained from the competition between volume and surface
tension contributions to the bounce action. At nonzero temperature,
this solution is unmodified until $2R_{c}>\beta$, that is, until
the bubble diameter exceeds the length of the compact direction
~\cite{Linde:1981zj,Garriga:1994ut}.
There are also some similarities with the problem of one-loop stability
of gauge fields at finite temperature in an external field, but the
mechanism there is different, and results from the competition between
positive contributions to the energy eigenvalues from Matsubara
frequencies with the negative contribution from the lowest Landau level~\cite{Meisinger:2002ji}.

\subsection{Morse-theoretic analysis}\label{sec:topo}

One of the striking features of our result for the decay rate,
associated with the behavior at thresholds, is the singular behavior
of the decay rate $\Gamma_{T}$. This singularity is due to the
factor
\begin{equation}\label{eq:singularity}
\left[1-\left(\frac{n\beta eE}{2m}\right)^{2}\right]^{-1/4}
\end{equation}
in eqns. \eqref{eq:Ksnp} and \eqref{eq:Klnp} for the fluctuation prefactors
$K_{np}^{(s)}$ and $K_{np}^{(l)}$. The origin of the singularity
can be understood at the classical level, however. In Figure~\ref{fig:action},
we plot $S$ as a function of the angle
$\theta$ for a family of paths with $n\beta m=1$ and fixed endpoint separation of $n\beta\hat{e}_{4}$.
Classical solutions are only obtained at the extrema, where $R=m/eE$,
and are given by $S_{n0}^{(s)}$ and $S_{n0}^{(l)}$. We see that
for $eE/m^{2}<2$, there is a local minimum corresponding to the short
path, and a local maximum corresponding to the long path. The instability
of the long path is obvious. At $eE/m^{2}=2$, the two extrema merge
and $n_{max}$ changes by one. The long and short paths are local maxima
and minima of the action, respectively, along a given direction in functional
space. Recall that $n_{max}$ is the greatest integer less than $2R/\beta=2mT/eE$.
When $2mT/eE$ is an integer, the long and short paths are degenerate,
and both are arcs of angle $\pi$ and arc length $\pi R$. If
$T$ is increased slightly, the degeneracy is lifted and a new maximum
and minimum of the action exist. The singularity in $K_{np}^{(s)}$
and $K_{np}^{(l)}$ is associated with the degeneracy of the two solutions.
This behavior is reminiscent of the behavior associated with the classical
spinodal, where a local maximum and minimum merge and the quadratic
approximation fails.

\begin{figure}
\centering \input{action.tex} \caption{\label{fig:action}The action $S$ for an arc solution as a function
of $\theta$ with $n\beta m=1$. Only the extrema, indicated by dots,
represent classical solutions, with the short path solution a local
minimum and the long path solution a local maximum. The values of
the action at the extrema are given by $S_{n0}^{(s)}$ and $S_{n0}^{(l)}$,
respectively. At $eE/m^{2}=2$, the two extrema merge.}
\end{figure}

This behavior is not restricted to the case of a constant, homogeneous electric field,
but will occur generally for an inhomogeneous electric field when the temperature
is nonzero and a zero-temperature instanton exists.

Morse theory provides a useful characterization
of the eigenvalues of second variation operators about a functional extremum
~\cite{morse1934calculus,Levit:1976fv}.
The \emph{caustic} is the envelope of trajectories obtained by fixing $x_\mu(0)$
and varying $\dot{x}_\mu(0)$. A \emph{focal point} of a classical path is defined
as a contact point between the path and the caustic surface. The central point
of Morse theory may be stated thus: the number of negative eigenvalues
of the second variation operator about a given classical path equals the number
of \emph{focal points} strictly between its endpoints, where each focal point
is counted with its multiplicity. This number is the \emph{Morse index}
of the path.

In the present case, all classical solutions are circles of constant radius $R=m/eE$.
Therefore, the \emph{caustic} is the union of a larger circle of radius $2R$ with
a single point at $x_\mu(0)$. A diagram illustrating this caustic is in figure \ref{fig:caustics}.
Zero-temperature wordline instanton solutions of winding $p$ (as well as our long
paths of the same winding) contact the caustic $2p+1$ times, which establishes their
imaginary contribution to the effective action. Short paths of winding $p$ contact the
caustic $2p$ times, which nets a real contribution to the effective action. In either case,
the $2p$ negative eigenvalues associated with additional windings result in an overall
factor of $(-1)^p$ in the prefactor, as shown in equation \eqref{eq:localpre}. The appearance
of such pairs of negative eigenvalues can be seen explicitly in the derivation of the
functional determinant prefactor for zero-temperature solutions (see Appendix \ref{sec:prefactors}).

We emphasize that these features do not depend on the exact shape of the wordline instanton
solution. Exact worldline instanton trajectories are known for several inhomogeneous field
configurations. These trajectories are no longer circles, but they are still closed and
periodic~\cite{Dunne:2006st}. This is sufficient to establish that the striking qualitative
features of our results -- the singularities and thresholds, as well as the fact that short
paths contribute to the free energy while long paths contribute the decay rate -- are expected
for inhomogeneous field configurations as well.

\begin{figure}
\centering \input{caustics.tex} \caption{\label{fig:caustics} A set of trajectories formed by varying $\dot{x}(0)$. The envelope of such trajectories is the caustic, indicated in red. A representative path is in blue. As the path touches the caustic, the fluctuation operator about it acquires a negative eigenvalue.}
\end{figure}

\subsection{Higher order effects}

We have seen in previous sections that the singularities in the effective
action result from the inadequacy of the Gaussian approximation at points in
functional space where two critical points become degenerate. At such points the quadratic
coefficient in the Hessian operator vanishes and higher order terms are necessary for a correct
computation of the effective action.
The inclusion of such higher-order effects is difficult even at zero temperature.
At finite temperature, higher-order effects will give rise to finite lifetimes
for quasiparticle excitations in the thermal medium.
These lifetimes may be calculated within the hard thermal loop
(HTL) framework~\cite{Braaten:1992gd}.
It is at least plausible that these finite lifetime effects smear out
the threshold singularities, rendering the decay
rate finite.
A complete calculation of this type is far beyond our grasp.
However, the singularities can be eliminated heuristically by including the effect of a damping rate for
the charged scalars. A damping rate for scalar QED can be obtained from a hard-thermal-loop
calculation of the imaginary part of the scalar self energy.
We include this effect by replacing
$m \rightarrow m - i \gamma$
in equation \eqref{eq:singularity}, where $\gamma \sim 0.04\, e^2 T $
is the scalar damping rate~\cite{Thoma:1996ag,Abada:2005jq}. This amounts to replacing the singular factor
\begin{equation}
\left[1-\left(\frac{n\beta eE}{2m}\right)^{2}\right]^{-1/4}
\rightarrow
\left[
\frac{
1 - \left(
          \frac{n\beta eE}{2m}
    \right)^{2}
    }{
      \Big(1 - \left(
                     \frac{n\beta eE}{2m}
               \right)^{2}
      \Big)^2 + \Big(\frac{2\gamma}{m}
                     \Big(
                          \frac{n\beta eE}{2m}
                     \Big)^2
                \Big)^2
    }
\right]^{1/4}
\end{equation}
in equation \eqref{eq:Klnp}.

In Fig.~\ref{fig:dampeddecayrate} we plot the total decay rate $\Gamma=\Gamma_{0}+\Gamma_{T}$
as a function of $T/m$ with the modified threshold behavior for the same three values of $eE/m^{2}$
used in Fig.~\ref{fig:decayrate}. As in that figure, the leftmost
part of each curve represents the contribution of $\Gamma_{0}$ alone,
which is independent of temperature. Each curve shows local maxima
at $T/m=neE/2m^{2}$. There is very little difference between the unmodified
and modified decay rates, except in the close vicinity of a threshold.
We have tried other modifications of the decay rate using the HTL damping
rate. the results are not sensitive to the particular modification used,
and the decay rate away from thresholds is virtually unchanged.
This indicates that the thermal contribution to the pair production
is substantially larger than the $T=0$ contribution once the first
threshold is crossed.

\begin{figure}[H]
\centering \input{dampeddecayrate.tex}

\caption{\label{fig:dampeddecayrate}
\label{fig:decayrate}The total one-loop decay rate $\Gamma=\Gamma_{0}+\Gamma_{T}$
divided by $m^{4}$ versus $T/m$ for various values of $eE/m^{2}$, including HTL damping effects.
The leftmost part of each curve represents the contribution of $\Gamma_{0}$
alone.
 }
\end{figure}

\section{Conclusions}

We have presented a first-principles worldline instanton method for calculating
the thermal contributions to Schwinger pair production in an
electric field, and argued that many of the features will
carry over to the case of inhomogeneous fields as well.
While the worldline formalism is powerful, it is physically opaque.
In Appendix~\ref{sec:equivproper}, we give a formal derivation of
our results by applying a saddle-point approximation to the standard
proper time representation of the effective potential for scalar bosons
in an external electric field.
 A simple physical understanding of these results analogous to the many physically
transparent derivations of the zero temperature decay rate would also be
highly desirable.

The decay rate shows unphysical behavior at a series of
thresholds, but this is an artifact of the Gaussian approximation
to the functional integral; we have shown that this behavior
is made physical by the phenomenological inclusion of
hard thermal loop effects. Once the first threshold for thermal
effects is crossed, the thermal contribution is larger than the
the $T=0$ contribution, rising as each successive threshold is
crossed. This strongly indicates the potential importance of thermal
effects in all such nonperturbative pair production processes.
We plan to extend this work to cases of more
phenomenological interest, such as quarks in constant
non-Abelian electric fields with Polyakov loop effects
included.

After the completion of this work, a paper appeared on arXiv~\cite{Brown:2015kgj}
that considers the same problem and has some overlap with our work.
However, there is significant disagreement between our results.

redpajama_set_name: RedPajamaArXiv


How Does Understanding God's Happiness Help Us Better Know Who He Is?
Randy Alcorn talks about how understanding God as a happy God will help us know Him better while he was interviewed on The Georgene Rice Show. For more information on this subject, please visit: http://store.epm.org/happiness/.


Newcastle City Council is preparing to set up a mutual organisation to take over its parks service, with substantial funding set to come from the public health department. The council has said it expects it will have no money for non-statutory services by 2017-18, reports Horticulture Week. The parks budget for the city has been cut by 70 per cent to £300,000 over the past three years. But council assistant director Tony Durcan said it is "not as bad as it might sound". The public health department is temporarily topping up the budget by £1m per year - enough to keep them going "while we sort out a different solution".
That solution is to create a mutual with charitable status that would care for the city's principal parks and major open spaces. It would be a self-governing independent body built on the contributions of local people and staff, with any profits made to be reinvested in parks. Permanent ownership of the parks would stay with the local authority but they would be leased for a peppercorn rent. The remaining parks would continue to be maintained by the council.
A mutual "can access opportunities and funding sources a local authority can't - such as trusts and foundations, which don't fund local authority projects or public health funding," Durcan explained. "It removes that feeling that if the parks are local authority-run, then the local authority pays. This new model draws on local people and partners - I think funders are more receptive to supporting it." Other funding such as development contributions from section 106 agreements would also be given to the mutual.
While finding funding to maintain parks is "clearly" a key reason for the change, "this is also about a new model of delivery, involving volunteers, local people and other organisations like businesses or the third sector in partnership", he added. Public health funding is likely to continue in some form and the public health department would have a bigger say in parks' governance.
"One of the things we're exploring is having parks as centres of therapeutic excellence - for example, patients being prescribed or referred to parks for fresh air and exercise," said Durcan.
Although this is not new - "clinical commissioning groups already have the capacity to do that if they think it's appropriate"
- Newcastle is exploring how health funding could in turn support parks in recognition that they are a public health asset. The next step is to commission a detailed business plan to look at funding sources and governance to ensure that it would work, followed by wider consultation.
Newcastle is also getting advice from the National Trust, which is working in Sheffield on setting up an endowment trust for the city's parks, as part of the Rethinking Parks programme.
"We think this is the right solution for Newcastle, but we need experts to test the financial model. If they come back and say yes, then we'll start doing the legals, look at how you create a mutual and look at questions of staffing and so on."
That would include how the city's parks staff - all in-house employees - would be employed under the mutual model. Durcan has a "very ambitious" target of handing the park over to the mutual in April 2017.


To make it easy for professionals and families to settle in Hong Kong as permanent residents, the Hong Kong Government introduced the Quality Migrant Scheme. An applicant can apply for an entry based visa for Hong Kong, migrate to the country as settle as permanent residents. To do so, professionals must be eligible, i.e. meet the requirements of Hong Kong immigration and labor market.
The experts verify your documents and ensure that upright documents are submitting with the application.
Hong Kong immigration demands an interview in Hong Kong, before one gets the PR visa. Assistance and guidance to face the interview will be provided.


text:
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June 4, 2020 July 8, 2020 Labour Hub Editors
Colonialism and Labour – from Attlee to Gaitskell
By Adam Peggs
Histories of the 'Bevanites', the grouping at the centre of the Labour Left in the late 1940s and 1950s, have typically focussed on a few topics. The personal journey of Nye Bevan and his unsuccessful bid for the Labour leadership, the Bevanites role in campaigning for nuclear disarmament and their resistance toward Labour's social democratic trajectory under Hugh Gaitskell. Often neglected is the relationships between the Bevanites— perhaps more properly called the 'Keep Left Group' — and the wave of anti-colonial campaigning in the 1950s and the early stages of British decolonisation. These events may hold significant lessons for the Labour left of today, including on the relatively substantial shortcomings of many of our ideological forebears.
The Bevanite line on international affairs very much grew out of the events of the immediate postwar years in which Labour was propelled into government by a landslide in 1945, becoming the great reforming government of the 20th century but failing to meaningfully shift British foreign policy. American historian Randy Rowan argues that the Attlee government, with Ernest Bevin as its Foreign Secretary, accepted 'the traditional assumptions of British foreign policy' in contrast to the left which hoped for a government which would 'abandon the traditional approach to foreign affairs and adopt policies and goals based on socialist principles'. These policies and goals could be described as follows: adopting a 'collective international security' system, a rejection of empire and support for independence movements in the Global South. This would also involve efforts to eliminate global poverty and opposition to an arms race, which would later be a key point of intention. These differences had been overcome in the manifesto by something of a fudge. On the one hand, Labour promised 'advancement' for India to self-government, on the other a gradualist tone was adopted — speaking instead of 'planned progress' for the lands Britain had colonised.
In Malaya, British authorities had declared a State of Emergency in June 1948 and rounded up roughly 4,500 people by the end of August, predominantly trade unionists. By September the events had led to the halving of the membership of the Pan-Malayan Federation of Trade Unions. These actions led to an open revolt against British rule.
In December 1948, the Labour government 'covered up' the massacre of a group of 24 unarmed Chinese civilians. In 1950, British authorities implemented the Briggs Plan, forcibly transferring half a million of the Malayan peasantry, one-tenth of the total population, into internment camps in stark contravention to the Geneva Conventions (which the military were aware of, but were not yet in force). This was followed by policies of collective punishment, including restricting food supply, against the camp's populations. While some sought to downplay these events as 'limited' collective punishment, they represent a major atrocity.
This seems less out of line with the fact that the 1942 crackdown on the Indian independence movement, which led to 10,000 deaths and 90,000 arrests, was enacted on the orders of then Deputy Prime Minister Clement Attlee. Half a decade later relatively little had changed, after British withdrawal from India had taken place the Attlee government's intention was to remain in control of the remainder of Britain's empire. Crucially, the Attlee government did ultimately grant independence to India, whereas some have argued Churchill would have resisted with force. Nonetheless, unfortunately it is easy to see this as the exception to the rule – there was ample continuity with the Conservatives approach to Britain's role in the world.
Into the 1950s
The changing situation in Malaya, in which Labour accused the new Conservative administration of 'strong arm methods' led to a shift in the party's approach, led primarily from the left. Woodrow Wyatt, then a left-winger, and Tom Driberg were both among those to issue loud condemnations of the government, with Driberg noting that the government's approach appeared to sought to starve Malayans and Wyatt comparing British actions to fascism. This led to a less combative condemnation of the Conservative's policy in Malaya, led by the left and signed by over 130 MPs, which accused the government of using tactics 'contrary to civilised practice'. It is worth noting the extent to which condemnations avoided criticising the Conservative's objectives, focussing instead on the means. Nor did this necessarily lead to a repudiation of the Briggs Plan, which one frontbencher praised and defended in parliament in 1952.
By this time the party was largely split on Malaya. Rowan argues that this was between two perspectives. One perspective, which included numerous former ministers under Attlee, the bulk of the trade union leaderships and much of the Labour-backing press, favoured self-determination in Malaya, but opposed left-wing calls for a quick timetable for independence and decried 'simple anti-imperialism' and left-wing 'catch phrases'. The other, formed around the Bevanites and a minority of the trade unions, called for a dramatic break with British foreign policy and denounced the British Empire. A vocal section of the left called for complete British withdrawal and gave unconditional support for Malayan independence, grounding both in a socialist and decolonial framework.
In 1953, Socialist Union — a 'moderate' group founded to oppose Bevanism — set out its perspective in detail in 'Socialism and Foreign Policy'. Here, they endorsed the goal of independence for colonised peoples and emphasised support for human rights and egalitarian goals, whilst warning against 'idealism' and calling for greater caution and a more 'realist' approach to foreign policy. In 1952, Socialist Union's publication Socialist Commentary argued against Bevanite demands for economic aid to be given to the Malayan population. In 1953, these divisions appear to have led to a unity motion from the NEC at Labour Party conference calling for decolonisation when 'the development of each territory makes it practicable'. The following year a similar motion was challenged with amendments by the left, who called for a more substantive commitment to decolonisation.
When Mohammad Mossadegh nationalised Iran's oil supply in 1951, in a bid to gain popular sovereignty over the countries' natural resources, Attlee imposed a blockade but rebuffed the idea of a full-scale coup against the Iranian government. Britain's Chiefs of Staff argued for a full military intervention against Iran. The Conservative-supporting press at the time railed against Mossadegh's actions, emphasising a view that Iran's oil was British property. In the Labour government, the Deputy Prime Minister Herbert Morrison had argued in favour of intervention, while Attlee, Chancellor of the Exchequer Hugh Gaitskell and Hugh Dalton had demanded caution going forward. Two years later, with Labour out of office, Britain's Conservative government and the United States did just that, removing Mossadegh and leading to the ascendency of a dictatorship. There were some sympathies with Mossadegh's actions on the British left, including in the pages of the New Statesman. Nonetheless, the Attlee government's policies in Iran appeared to receive little noteworthy opposition from inside the party and little changed when their Conservative successors deposed the Iranian government in August 1953. Whether the economic significance of British oil interests in Iran, and the value this represented to the exchequer, helped to mute criticism is unclear — though Attlee's Foreign Secretary Ernest Bevin had emphasised the prime importance of Iran's oil supply to Britain's strategic interests.
Throughout the 1950s a budding anti-colonialism began to appear on the British left. Organisations such as the Movement for Colonial Freedom and War on Want sprang up and found support and participation from members of the Parliamentary Labour Party. The Movement for Colonial Freedom (MCF) was founded in 1954, as an amalgamation of existing anti-imperialist groups including the Congress of People's Against Imperialism. Among its founding members were Fenner Brockway, an MP and former General Secretary of the Independent Labour Party, and Tony Benn, who became the MCF's treasurer. Among the group of MPs to advance its causes in Westminster were Barbara Castle, Harold Wilson. African National Congress leader Oliver Tambo, anti-apartheid activist Ruth First and George Padmore all played important roles in the organisation. The group would go on to be fundamental in the foundation of the Anti-Apartheid Movement.
The MCF were pivotal in pushing Labour toward coming out in opposition to the Suez War. Gaitskell had initially, during June 1956, favoured the use of force against Gamal Abdel Nasser in what would soon become the Suez conflict and decried Egypt's seizure of the Suez Canal as 'totally unjustifiable'. But over the summer Gaitskell had shifted toward favouring United Nations backing before any British assault on Egypt went ahead. This was in distinction between the position set out by the likes of Konni Zilliacus, Tony Benn and Richard Crossman — with Zilliacus accusing Tory MPs of only paying 'lip service' to the UN Charter and engaging in imperialistic 'power politics'.
When Britain attacked Egypt without UN approval and without the support of Commonwealth nations or the United States, Gaitskell attacked Eden in strong terms accusing him of 'disastrous folly' and stating that Labour would oppose the war by any constitutional means. Nonetheless, Gaitskell's statements had a notable focus on the extent to which the war would damage Britain's reputation, potentially undermine British influence and damage the Anglo-American alliance. Elsewhere in the party, the denouncement of the government was even fiercer. On a televised debate Michael Foot accused a Tory Member of Parliament of being a 'criminal', for his support for the war — allegedly almost coming to blows. Two days later, Labour and Tory MPs nearly brawled in Westminster after Eden was compared to Hitler and denounced as a 'murderer' and Gaitskell accused of betrayal.
The MCF, having already been vital in fostering anti-colonial sentiment in British politics, became the key player in organising the anti-Suez War protests which the Labour Party and TUC would later take over. While US pressure on the Conservative government is generally perceived to be the primary cause of British withdrawal from the war, the popularity of the Labour-led protests was also not insignificant as a factor.
British Repression in Kenya
The struggle for Kenyan independence proved to be a significant driver of changing political attitudes at home. From 1952 onward, British colonial authorities had been fighting the Kenya Land and Freedom Army, in an effort to crush Kenya's independence movement.
British repression in Kenya has also left a long and disturbing legacy, influenced by the repressive Brigg's Plan used in Malaya and involving forced labour camps and widespread and extreme use of torture — the crimes have since been compared to the gulag.
In the early 1950s British actions in Kenya, purported to be in opposition to the "Mau Mau" rebels (a term invented by British colonial authorities), were routinely denounced by Barbara Castle, Richard Crossman, Tom Driberg and Labour's former Colonial Secretary Arthur Creech-Jones. Harold Wilson, who had been noted by some for his keen interest in anti-colonial politics, would go on to cover up British crimes during his tenure as Prime Minister.
Castle, for her vocal denunciations of British action, found herself widely denounced by both Conservative MPs and the British press for her position, in particular for her series of articles covering the subject for the Daily Mirror in 1958. In the era's moral panic about "Mau Mau" rebels, dubbed the 'face of international terrorism' by one scholar, figures like Castle were perceived to be on the wrong side and ultimately undermining the national interest. Even outside of the Conservative right, Castle's anti-colonial campaigning was perceived to be flawed and even wrong-headed, with the future cabinet minister dubbed 'obsessive' and 'doctrinaire' for her views and actions. Her denunciation of British rule in Kenya as an unjust 'police state' guilty of 'murder and torture' did not endear her to those in the party who preferred not to rock the boat.
Anti-Kenyan sentiment on the political right was particularly pronounced, with racist and imperialist depictions of Kenyans as cannibals prominent in the British press. In a return of classic colonial narratives demands for Kenyan self-determination were deemed to be illegitimate as Kenyans were portrayed as not 'civilised' and as lacking legitimate political leadership'. Many of the documents relating to the camps were destroyed in 1963 when Britain withdrew from Kenya (four years later the Wilson government would deny the existence of another batch of papers).
By some accounts, the Labour Party's pressure at home, spearheaded by the likes of Castle, no doubt alongside the conflict abroad, pressured the Conservative government to announce its intention to end British rule over Kenya. Nonetheless, it is crucial to emphasise British rule in Kenya was not simply ended by the activities of parliamentarians.
During this period the internationalism of left parliamentarians rarely strayed past the limits of liberal rule-of-law approaches. For instance failing to fully grasp the vast disparity in economic power between the 'advanced' industrialised countries on the one hand and the countries of the Global South on the other. This is crucial for understanding the political thought in the PLP during the period, frequently seeing the priority of international foreign policy as upholding the rules-based system rather than pursuing an ethical and anti-racist foreign policy for its own sake.
Toward a new internationalism
In 1985, Ralph Miliband and Marcel Liebman lamented the long history of British social democratic leaders in the 1940s and 1950s failing to show solidarity with those colonised by the British Empire. Highlighting the examples of Kenya and Malaya among others, they argued leadership's had repeatedly failed to uphold the principles of internationalism. On examination, it is hard not to come to similar conclusions – especially with regard to the Attlee administration. These serious failings from decades ago are also instructive in illustrating the need for the recasting of the party in a left-wing direction and the scale of that task.
The Gaitskellites and many of the veterans of the Attlee government focussed on a 'realist' approach and went very much with the grain of British foreign policy, albeit with a medium or longer-term objective for decolonisation. In part this may have related to the extent to which the postwar welfare state was perceived to be reliant on the economic power derived from Britain's Empire. The Bevanites and the left-wing trade unions cultivated an anti-colonialism of sorts, refusing 'to accept the whole substructure of British foreign policy' as Anne Perkins has put it, though it often fell short from what might be required. After all, it risked building up an approach to international policy which treated British parliamentarians as the vanguard of a just foreign policy, rather than just one facet of a broader anti-colonial movement.
The left today has a role to play in opposing a foreign policy which overwhelmingly focuses on shoring up Britain's status as a major military power, and maintaining British state and economic power. And in ensuring that the Labour Party is not sucked into defending those interests in the name of 'credibility', patriotism and bipartisanship. If the party cannot meet these tests in opposition, it will have zero chance of doing so in government – given the pressures of government it will likely be worse. This means thinking critically about the real role of British foreign policy, strengthening links with anti-war, human rights and decolonial movements, and learning from them. While the formal empire is now gone, the material relations that underpinned it have not. The Corbyn era has shown the sheer pressure which can be brought to bear upon the party when Labour attempts to challenge Britain's foreign policy orthodoxies, counteracting these pressures will only be more of a challenge in the 2020s. Much has changed over the last sixty years, but Britain remains one of the wealthiest nation-states in the world and an influential power, as such there is still much to learn from both the successes and the serious limitations of Labour's postwar foreign policy.
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redpajama_set_name: RedPajamaCommonCrawl


text:
ERIN HARPE & THE DELTA SWINGERS
"Electric Boogie, Blues & Beyond!"
"Erin Harpe is a knockout."
–Robert Feuer, KGGV-Occidenta (CA)
"Delightful delivery and positively top-notch fretwork… about as good as it gets!"
–Blues Magazine (Netherlands)
2019 New England Music Award-Winning "Blues Artist Of The Year"
International Blues Challenge Semi-finalist (2019, 2017, 2013 & 2011)
"Blues Artist of the Year" from the Boston Music Awards (2012)
Boston Blues Challenge Winner (2018, 2016, 2014, 2012 & 2010)
Boston Music Award Nominee (2018, 2012, 2011, & 2010)
Erin Harpe & the Delta Swingers were just named New England's best blues band, winning "Blues Artist Of The Year" at the 2019 New England Music Awards! Singer/guitarist Erin Harpe leads the roots-rocking electric band on vocals and lead guitar, playing a mix of styles they call "Boogie, Blues & Beyond". A rising star in the roots and blues scene with a growing fan base around the world, she's been called "one of the most dynamic, talented and exciting roots rocking blues women on the scene" by Living Blues Magazine, and has been compared to legendary blues women like Bonnie Raitt and Rory Block. The Midwest Record even called her "Bonnie Raitt on modern performance enhancing drugs!" The "modern blues mama for our times" has had an exciting year, from winning awards, to competing solo at the International Blues Challenge in Memphis (where she made it to the Semi-Finals!), to touring around the US – with stops at the Rhythm & Roots Festival (RI), Tall City Blues Fest (TX), Musikfest (PA) and Paw Paw Fest (OH), as well as in the UK! This holiday season Erin and the band celebrate with a limited-edition vinyl release of their album "The Christmas Swing" and a string of holiday parties.
"The Christmas Swing" is Erin Harpe & the Delta Swingers' self-produced, critically-acclaimed (anti-) Christmas album. This season on VizzTone/Juicy Juju Records, the album will be released on limited edition vinyl! The album, which has been called "sassy" and "un-traditional", made it to #2 last season (Eric Clapton was #5!) on the Roots Music Report's Top 50 Holiday Album Charts, AND #17 on the Living Blues Charts last December! Featuring ten songs – including a couple of Erin's originals and her own arrangements of traditionals and songs by Chuck Berry, Bessie Smith, Lightnin' Hopkins, Leadbelly, and more – the album is a great alternative seasonal romp, chock full of hooky blues-guitar-fueled gems that you'll want to listen to each year as the holidays approach – in fact Steve Jones of Blues Blast Magazine says, "I will be giving it many more spins this holiday season and beyond."
Band history and releases:
In 2010 Erin and her husband, bass player Jim Countryman, started Erin Harpe & the Delta Swingers, an electric delta blues-inspired quartet. They were off to a great start right away, winning the Boston Blues Challenge that same year and being christened "Charles River Delta Blues" by the local media. They were signed to blues label VizzTone in 2014. In the past 9 years the band has gone electric and branched out to created their own sound, dubbed "boogie, blues and beyond" – an electrifying original sound that takes you from the delta to the dancefloor mixing in funk, soul and reggae swing!
Erin Harpe & the Delta Swingers have released three albums, all of which have done very well on radio charts, receiving critical acclaim from media around the world. Love Whip Blues (2014) received 4 stars in DownBeat Magazine and was featured on SiriusXM's Bluesville, and the band's sophomore album Big Road (2017) made the TOP TEN in Roots Music Report's Contemporary Blues Albums chart, the iTop Top 100 Blues Albums AND Relix Jamband Radio Charts. The band's first holiay album, The Christmas Swing (2018), made it to #2 on the Roots Music Report's Top 50 Holiday Album Charts (Eric Clapton's holiday album was #5!), as well as #17 on the Living Blues Charts in December!
Erin has also put out two acoustic blues albums, Blues Roots (2002) and Delta Blues Duets (2008) – an album of duets with her dad – in between touring and releasing five albums with her rock band Lovewhip (with hubby/bass player Jim Countryman). Erin's soulful vocal style and accomplished finger-picking guitar playing has earned her many fans, including guitar greats Ronnie Earl and Billy Gibbons, and she is quickly becoming recognized on the international blues scene.
Early history:
Growing up in Maryland, Erin learned finger-style blues guitar from her dad, visual artist/guitarist Neil Harpe, as well as from watching local piedmont blues luminaries such as John Cephas & Phil Wiggins, John Jackson, Eleanor Ellis, Warner Williams and others – at the famed Archie's Barbershop. Later moving to Boston, Erin put out two acoustic blues albums, Blues Roots (2002) and Delta Blues Duets (2008) – an album of duets with her dad – in between touring and releasing five albums with her rock band Lovewhip (also with hubby/bass player Jim Countryman). After being invited to play NotSXSW (John Conquest's Americana answer to South by Southwest) as a solo artist a few times, Erin and Jim decided it was time to start a blues band, and The Delta Swingers was born! In their first year as a band, they won the Boston Blues Challenge, and were in Memphis for the first time at the International Blues Challenge. While there, the band was asked to play the prestigious VizzTone Showcase at the Rum Boogie on Beale St. In the excitement of trying to impress the crowd, in the middle of the first song, Erin accidentally kicked over her acoustic guitar, breaking it's neck. Luckily the host, Bob Margolin (Muddy Waters Band), was there, and what came next changed everything. He bestowed Erin with his Gibson Les Paul gold top electric guitar, and the band went electric. Since then, Erin has honed her sound, and her favorite electric guitars are her prized Epiphone Wilshires and her custom-made Karge Bel Aire, with a Marshall Origin tube amp.
Photo by Kevin Umlauf.
"Erin Harpe... has it all — a golden voice and the guitar chops that dazzle. As many of the great divas of the roots rocking blues are aging, the emerging new generation, like Imelda May, Grace Potter and Erin Harpe are firing up younger audiences, and Erin makes it as fun and exciting as ever, and that's a good thing for the blues."
–Living Blues Magazine
"Easily Bonnie Raitt on modern performance enhancing drugs, Harpe is blues mama for our times. Killer stuff..."
–Midwest Record
"Erin Harpe is a hunter and gatherer... collecting the sounds as her branded version of Delta Blues, reimagining and reworking the music."
–Alternate Root
"Harpe is delightful. She creates a happy vibe reminiscent of Hot Tuna... for those looking for a really good time."
–Richard Ludmerer, Making a Scene
"★★★★ Avoiding the perils of predictability, these four New Englanders craft a fresh, genre-crossing group sound…" -DownBeat Magazine
"Erin Harpe is a hot mama blues singer." –Sing Out!
"Grabs the senses with a power and beauty... Harpe is a very fine guitar picker, with a great grasp of the ragtimey-blues feel and tradition in particular. Her voice is glitzy and grounded in the tradition too..." -Iain Patience, Elmore Magazine UK
"They won me over with a sound that harkens back to the time of juke joints, with some modern funk and rock woven in. Erin Harpe's got a righteous set of pipes and plays a mean guitar and the rest of the band has a whole lot of awesome going on." –Aimsel Ponti, MaineToday's Face the Music
"Something akin to what the blues sounded like, Muddy and his band plugged in, which sounds better than ever in these hands." –Cheap Thrills Boston
"A singular brand of blues... Harpe is an amazing talent and the band is a revelation." –George Lenker, MassLive.com
"Fine musicianship" –Blues Matters (UK)
"Erin Harpe has it all. The looks, the chops, the voice, the presence and the band all add to an aura that mesmerized the crowd..." –The Alternate Root Magazine
"This blues chanteuse breathes new, whiskey-soaked life into the likes of Memphis Minnie and Kansas Joe, with a sound that's uniquely Charles River Delta." –Boston's Weekly Dig
"A dance band that has a unique delta blues flavor and a world music creamy filling... mixing in afrobeat, reggae, funk, and disco with delta blues finger-picking, creating an amazing new sound." –Phil Simon, Live Music News and Reviews
holiday album
Sophomore Album


The September/October, 2006, issue of FGBC World, the all-Fellowship publication for Grace Brethren churches, is arriving in homes and churches this week. Here is promotional copy you may use for bulletins, newsletters, websites, and other church communications. Please pass along to your church staff. See the AGBM blog for distribution suggestions.
Larry Everett of the Grace Brethren Church of Clinton, Maryland, remembers his "taste of hell" as a firefighter at the Pentagon on September 11, 2001. Read about how God answered the prayers of this man and has been working in his life since in the September/October issue of FGBC World, now available. Take a copy today or read it online at www.fgbcworld.com.
More than 2,500 teens gathered at Biola University in LaMirada, California, for BNYC July 22-28. The "Rescue" theme for the conference was based on Colossians 1:13-14. Also, the Celebrate06 adult conference, held July 29-August 3 in Indian Wells, California, discussed the theme "Hearts on Fire." Read more about what happened at conference this year and see the photos in the September/October issue of FGBC World, now available. Take a copy today or read it online at www.fgbcworld.com.
Pike Grace Brethren Church of Johnstown, Pennsylvania, works with the Johnstown Grace Brethren Church to reach the inner city children through VBS. Read about what God did in and through both these churches in the September/October issue of FGBC World, now available. Take a copy today or read it online at www.fgbcworld.com.


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Asia-Pacific, Civil Society, Development & Aid, Economy & Trade, Editors' Choice, Europe, Featured, Food and Agriculture, Global Geopolitics, Global Governance, Headlines, Labour, Natural Resources, Population, Poverty & SDGs, Projects, Regional Categories, TerraViva United Nations, Trade & Investment, Water & Sanitation
Inside Pakistan's Untapped Fishing Industry
By Zofeen Ebrahim	Reprint | | Print |
According to the World Wide Fund for Nature (WWF)-Pakistan, nearly 400 million gallons per day of untreated waste from Karachi goes into the sea, making a fisherman's job an extremely dirty one. Credit: Zofeen Ebrahim/IPS
KARACHI, Nov 4 2014 (IPS) - If you want to know what 'sea traffic' looks like, just go down to the Karachi Harbour. Built in 1959, the dockyard houses close to 2,000 big and small boats anchored in the grey sludge at the edge of Pakistan's southern port city, which opens into the Arabian Sea.
Life on the jetty, an all-male domain, is anything but dull. The air is thick with the smell of fish. With anywhere from 100,000 to 150,000 men working here on a given day, mornings are crowded and noisy with vendors auctioning and buyers inspecting the catch.
Loading and unloading of goods continues uninterrupted well into the afternoon; boats are being geared up for the voyage – rations are inspected, fuel, water and ice are stocked, last minute checks of the nets, the ropes and the engines are underway.
Fishermen operating off the Karachi Harbour in southern Pakistan can earn up to 15,000 rupees (about 145 dollars) per month, but their income is dependent on their catch. As a result, many fisher families live in poverty. Credit: Zofeen Ebrahim/IPS
At one end of the harbour, mammoth-sized wooden arks lie in various stages of completion. Close by, fishing nets are being newly woven or repaired. A medium-sized boat (45 to 55 feet in length) carries anywhere from 20 to 25 fisherman; they go deep into the sea for a maximum of a month.
The income fluctuates – if the catch is good each fisherman can earn as much as 15,000 rupees (about 145 dollars) that month, but there is no fixed salary. These men only get a percentage based on their haul. There is a ban imposed by the government during the months of June and July because it is the best season for prawns, the mainstay of the fishery industry here in Pakistan.
Every day some 2,000 boats jostle for space in the murky waters of one of Pakistan's oldest harbours. Credit: Zofeen Ebrahim/IPS
The Exclusive Economic Zone (EEZ) covers an area of about 240,000 sq km and the maritime zone of Pakistan, including the continental shelf, extends up to 350 nautical miles from the coastline.
Thus the country has the potential to become a major producer of seafood, not only for local consumption but for the global market as well. Currently, nearly 400,000 people are directly engaged in fishing in Pakistan and another 600,000 in the ancillary industries.
A fisherman walks in front of one of the many half-constructed wooden arks that lie strewn about the Karachi harbour. Credit: Zofeen Ebrahim/IPS
However, an industry that can earn valuable foreign exchange and create a huge job market contributes a dismal one percent to Pakistan's GDP, with annual exports touching just 367 million dollars in 2013-2014, primarily to countries like China, the United Arab Emirates (UAE), Thailand, Saudi Arabia, Malaysia, Indonesia and Korea.
The average annual catch is almost 600,000 metric tons of more than 200 commercially important fish and shellfish species, found in and around the Karachi Harbour.
Illegal nets made of fine mesh end up trapping small, commercially unviable fish in massive quantities. Between 70 and 100 trucks, each loaded with 10,000 kg of trash fish, leave Karachi's harbour each day. Credit: Zofeen Ebrahim/IPS
"This includes the catch from other harbours, even from Balochistan [located on the south-western coast], all of which comes here to be sold inland or exported," says Sagheer Ahmed, spokesperson for the Karachi Fisheries Harbour Authority (KFHA).
One way to increase the role of fisheries in national GDP, says Muhammad Moazzam Khan, ex-director general of the Marine Fisheries Department, is to put a stop to over-exploitation of fish stocks.
The harbour is an all-male domain. Anywhere from 100,000 to 150,000 men work here on any given day. Credit: Zofeen Ebrahim/IPS
What was once an indigenous occupation, small fishermen say, has turned into a greedy enterprise, resulting in overharvesting of marine resources.
Kamal Shah, spokesperson for the Pakistan Fisherfolk Forum, a non-governmental organisation working for the rights of the local fishing community, says, "The indigenous people know how to recharge the marine life; they respect nature and follow the principles of sustainable livelihood, which seems lost on those who want to get rich quick."
Before heading out to sea, fishermen gather in groups to see to the final details of their voyage: stocking up on food, checking the engines and repairing their nets. Credit: Zofeen Ebrahim/IPS
Khan, currently a technical advisor to the World Wide Fund for Nature (WWF)-Pakistan, worries about extinction of several marine species. He lamented the depletion of shrimp, lobster, croaker, shark and stingrays due to over-exploitation.
"Recovery of these resources is very slow and even if these fisheries are closed down, it would still take decades to restore their stock," he says.
Nearly 400,000 people are directly engaged in fishing in Pakistan and another 600,000 are involved in the ancillary industries according to the Karachi Fisheries Harbour Authority (KFHA). Credit: Zofeen Ebrahim/IPS
Activists, like Shah, say a major problem is the use of illegal (fine mesh) nets that end up catching juvenile fish as opposed to the government-approved nets for deep sea and creek fishing.
These illegal nets literally sieve undersized fish that are economically not viable, but nevertheless important for keeping the marine ecosystem balanced.
Ahmed of the KFHA says Pakistan exported 50 million dollars worth of "trash fish" in the last financial year. "As many as 70 to 100 trucks each loaded with 10,000 kg of trash fish leave the KFHA every day," he explains.
The WWF-Pakistan is worried about the extinction of several marine species. Experts are particularly concerned about the depletion of shrimp, lobster, croaker, shark and stingrays due to over-exploitation. Credit: Zofeen Ebrahim/IPS
Shah also blames the "industrial waste from factories and organic waste from the cattle colony" that goes untreated into the sea. According to the WWF-Pakistan, nearly 400 million gallons per day of untreated waste from Karachi goes into the sea.
But there is some good news for Pakistan's fishing industry.
After blocking fish exports for six years, last year the European Union (EU) de-listed two of the more than 50 Pakistani companies and this year it is hoped another five will get the green signal. "More than 20 percent of the fish export went to the EU," according to KFHA's Ahmed.
Male children are roped into their father's occupation very early in life, when they are taken onboard the ships as helpers. Few fisher families send their kids to school. Credit: Zofeen Ebrahim/IPS
An ineffective cold chain and low standards in traceability (tracking the supplier, date and time of transactions) were identified as major issues.
"Boats did not meet the specifications. Often the wooden floor and the wooden containers where catch was stored did not meet the hygiene standards, machines used to haul the net often leaked oil on the floor and the fish hold was found to be rusty," Ahmed says.
Today nearly 1,000 boats have been modified. Fiberglass cladding in the fish-holds and the increased use of plastic crates have replaced wooden containers. This has also helped maintain the temperature required to keep the catch fresh.
The fishermen perform multiple tasks on the boat. This man makes fresh rotis (flat bread) from whole-meal flour, which the men eat with the fish they catch. Credit: Zofeen Ebrahim/IPS
In addition, processing and packaging factories have started tracking the catch to adhere to the EU's condition of traceability of the catch.
While Pakistan is slowly reclaiming the EU market and has found its foothold in newer ones, it has a long way to go before establishing itself as a world-class fisheries hub.
Perhaps most importantly it will have to tackle increasing pollution that has decimated some of the most important fishing grounds along the Karachi coast. Similarly, it will have to combat the kind of environmental degradation caused by land reclamation and mangrove denudation, both of which reduce natural levels of productivity along the coast, especially in the Sindh province.
Edited by Kanya D'Almeida
Follow @IPSNewsUNBureau
Millennium Development Goals (MDGs)
Pakistan Fisherfolk Forum
Poverty & MDGs
World Wide Fund for Nature (WWF-Pakistan)
fortunev
What a frigging unhealthy mess.


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Diospyros lateralis is a tree in the family Ebenaceae. It grows up to  tall. Inflorescences bear up to three flowers. The fruits are round to ovoid, up to  in diameter. The specific epithet  is from the Latin meaning "lateral", referring to the position of the inflorescences on the stem. Habitat is lowland mixed dipterocarp forests. D. lateralis is found in Thailand, Sumatra and Borneo.

References

lateralis
Plants described in 1873
Trees of Thailand
Trees of Sumatra
Trees of Borneo

redpajama_set_name: RedPajamaWikipedia


Here in Frisco, Colorado, November always starts out as the slowest, quietest month. So you might not believe it if you were walking down Main Street today, but very soon this place will be bustling with people!
Frisco's Tree Lighting is on Friday, November 28 at 5:30 pm. We'll be open until 8 pm that night, so come warm up with some wassail afterwards!
We'll be closed all day on both Thanksgiving and Christmas.
Enjoy the holiday season! We hope you will come and visit us at Frisco Fun & Formal!


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Clicky Media launches free event to boost girls in tech
by Simon Austin
Digital marketing agency Clicky Media is joining forces with Liverpool Girl Geeks and UKFast to host OMG! Girls in Tech, a free event designed to kickstart careers for women in the digital and tech industries.
The free event is targeted at women aged 18 and over and will feature workshops, networking and talks at the UKFast Campus in Manchester on 28th October.
Delegates will be able to hear from inspiring women across a broad range of industries, including keynote speaker Kate Willard, Head of Corporate Projects for Stobart Group.
Oliver Yeates, founder and CEO of Clicky Media, said: "We are always looking to inspire people to get involved in the digital and tech industries, as it is something we are extremely passionate about.
"With 50% of our team made up of females - which is very unusual for the industry - we go out of our way to encourage talented women to join the team and are constantly striving for equality, knowing from experience what a vital and talented contribution they are making.
"I believe that nurturing and encouraging women to start a career in this industry is essential to fill the gap between the jobs available, which is set to grow exponentially in the coming years, and the demand for qualified graduates in digital and tech.
"Many girls express an interest from a young age and yet, currently, only 7% of girls take computer studies at A' Level and only 17% of those studying computer science in higher education are women.
"We want this to change and hope that the exceptional line up that we have planned for the OMG! Girls in Tech event will be the catalyst for change."
NewsDigital Agency News
Fluid Commerce appoints head of marketing as it targets £1.9m turnover
Two senior appointments at Manchester's Numagoo
Cerisola to lead new PR division at Mediaworks
PPC Analyst
Integrated Marketing Analyst
Group Marketing Manager
PM Law Group
Hydra Creative
Banana Kick


Kudos to amazing young dyslexic entrepreneur Max Ash who came up with an idea of sports-themed cups and bowls that could be created with the help of a 3D printer when he was just 8 years old. By the time he was the grand old age of 11 years, he had already won a Babson College pitch contest, raised $6000 in a crowdfunding campaign, then caught the notice of Uncommon Goods which placed a large order. Today his mugs can be found in Hammacher Schlemmer, Nordstrom, and the Basketball Hall of Fame!
Max definitely has the Dyslexic Advantage – but wait – there's even more, Max has been donating to Dyslexia charities (and most recently to Dyslexic Advantage – Thanks Max!) and other non-profits in addition to saving for college.
Bravo to Max and his family! Max's website is HERE.


The agency was asked to come up with a concept to utilize the then-new Facebook Canvas platform. I hopped on to concept and create canvases to showcase three elements of the Pacifica: Award-Winning Safety Features, Design paired with Technology, and the environmentally conscious Hybrid version.
The mandate was to explore all the available features a canvas could offer, provided the assets allowed for it. After experimenting with the platform a bit, I had to come up with a creative work-around in order to make the ad feel like it was worth spending time with. The "Tilt" feature was a fun way to surprise a user and let them interact, but it only supported images, no video. In order to further surprise and delight the user, I exported an animated GIF into the tilt module.
The work was well received and a blast to make!


With this information, you can market your business using email. Make sure your content is very interesting and catches people's eyes. Think about what you would like to see as a consumer and then appeal to that. The fruits you will yield and the speed with which they arrive will shock you.


The term carrying capacity may have first appeared in an 1898 publication by H. L. Bentley of the United States Department of Agriculture, with an original focus on maximizing production of domestic cattle on rangelands of the US southwest. The first use in wildlife management was apparently associated with classic studies of deer populations on the Kaibab Plateau in northern Arizona in the 1920s. The concept was popularized in wildlife ecology by Aldo Leopold and Paul Errington in the 1930s.
There have been four typical uses of carrying capacity in applied ecology, illustrated in Figure 2: (1) the maximal steady-state number or biomass of animals an area can support in the absence of exploitation (the original use of carrying capacity, K); (2) the maximal sustainable yield (MSY) of biomass of animals an area can produce for exploitation, which equals 0.5K in the simplest form of the logistic model; (3) the maximal sustainable economic yield (MEY) of animals an area can produce for exploitation, which equals the maximum difference between yield value and cost of exploitation; and (4) the open-access equilibrium (OAE), where the value of the yield equals the cost of exploitation, which is the upper economic limit of exploitation in the absence of economic subsidies and restrictive management regulations. Note that open access, typical of historical marine fisheries, often leads to severe overexploitation because the population is reduced to sizes far below the other types of carrying capacity. Indeed, even the application of maximum sustainable yield in single-species fisheries management has proven elusive and often disastrous, as evidenced by the poor state of most marine fishery stocks so managed.
Figure 2 Four definitions of carrying capacity used in applied ecology. Yield (or so-called surplus production, which directly translates to gross profit and which varies directly with the growth rate of the exploited population) initially increases and eventually decreases as exploitation effort increases, whereas the cost of exploitation presumably increases linearly with effort. The conventional carrying capacity (K) occurs in the absence of exploitation (i.e., zero effort). MSY occurs where total yield peaks (i.e., 0.5 K in the logistic model). MEY occurs where net profit (i.e., gross profit minus cost) is maximal (i.e., where the slopes of the cost and yield curves are identical). The OAE occurs where gross profit equals cost. Typically, as illustrated, K> MEY> MSY> OAE.
sheep, etc. The Society for Range Management defines the term as the maximum stocking rate possible which is consistent with maintaining or improving vegetation or related resources. A more general definition is the optimum stocking level to achieve specific objectives given specified management options. These practical definitions implicitly acknowledge that carrying capacity is not a constant, but rather is affected by a variety of environmental factors.
where A is the number of animal-unit-days an area can support ((# x d) per square kilometer), B is biomass of food in the area (kg km-2), C is the metabolizable energy of that food (J kg-1), and D is the metabolizable food energy required per animal unit per day (J/(# x d)). Obviously, such formulas ignore the reality of environmental variation, species interactions, etc.
A classic field study of wildlife carrying capacity was published by David Klein in 1968. In 1944, some two dozen reindeer were released on St. Matthew Island in the Bering Sea, where previously there had been none. Lichens were plentiful and the population increased at an average rate of 32% per year for the next 19 years, reaching a peak of about 6000 in 1963. During the severe winter of 1963-64, nearly all the animals died, leaving a wretched herd of 41 females and 1 male, all probably sterile. It was not so much the inclement weather that devastated the herd as it was a deficiency in food resources caused by overgrazing. After careful study, Klein concluded that 5 reindeer per square kilometer would have been the carrying capacity of an unspoiled St. Matthew Island. An animal census taken in 1957 gave 4 animals per square kilometer. A further 32% increase during the ensuing year brought the population to 5.3 per square kilometer, in excess of the predicted carrying capacity and a prelude to the eventual population crash.


NEW ORLEANS – A Louisiana-based contractor lost its appeal of the dismissal of its due process challenge for failure to state a claim.
Nobles Construction LLC filed suit against Richard N. Thomas Jr., individually and as President of Washington Parish, Leo Lucchesi, individually and as Director of Public Works for Washington Parish, Charles E. Mizell, individually and as Mayor of City of Bogalusa, Landworks Inc. and the City of Bogalusa after a dispute over contracts for the maintenance of a landfill. The case was dismissed by a district court and Nobles appealed.
Although Nobles had the lowest bid, the contract was awarded to Landworks Inc. the company that had managed the landfill since its inception in 1995. Nobles claimed that Louisiana's public bid law applied to the proposal and required the parish and city to accept the lowest bid. In the original suit Nobles requested either a reopening of the proposal process or to be awarded the contract. The company also sought damages alleging that its due process rights had be violated.
The district court that found the legal process available to Nobles was sufficient and that the Parish's and the City's alleged behavior was not so outrageous as to constitute a violation of substantive due process.
The U.S. 5th Circuit Court of Appeals agreed in an opinion released by Circuit Judges Edwin Smith, Edward C. Prado and Stephen A. Higginson per curiam. The court cited a similar case, Marco Outdoor Advertising, Inc. v. Regional Transit Authority, as precedent for showing that Nobles was provided with adequate legal process to challenge the actions of the Parish and City. Nobles argues that Marco was incorrectly decided, but the court cannot overturn the decision of another panel.
In order to show a substantive due process claim, Nobles needed to prove that state officials "acted with culpability beyond mere negligence." Nobles claims that the city refused to discuss the bidding process, didn't require Landworks to comply with all proposal specifications, overlooked material omissions in Landworks proposal and that Landworks' owner took the mayor on a golf trip out of state. It further claims that these allegations constitute a substantive due process violation.
Similar allegations were made in Marco, but as in that case, the court found that the decision of state officials was "not so arbitrary so as to shock the conscience" The panel concluded that the district court was right to rely on precedent and dismiss the case.


Christian Siriano is the latest designer to offer to dress Bebe Rexha for the Grammys after fans got in touch with the inclusive fashion star.
Bebe called out the fashion world on Monday, revealing she can't find a designer to dress her toned U.S. size 8 (U.K. 12) frame because they deem her "too big" to wear their creations.
While she didn't name names, she let the people in question know that she is now no longer interested in wearing their outfits.
Numerous labels have since reached out and offered to dress Bebe, who is up for two awards at the annual prize giving on 10 February (19), with Christian the latest to get in touch.
"Thanks everyone for thinking of us. We have dressed @beberexha a few times and would be happy to do it again for her," he wrote on his social media accounts.
Christian previously swooped in when Ghostbusters actress Leslie Jones publicly revealed no designers would dress her for the premiere of the rebooted film franchise.
Since winning reality TV competition Project Runway in 2008, the 33-year-old has become known for his inclusive attitude to style and fashion.
Michael Costello has also offered up his designer services.
"I don't blame her for being upset, I've been friends with Bebe for a really long time, I'm sad that she didn't call me first because I would have said yes," Michael told TMZ. "But I still offer to dress Bebe.
August Getty, Tanya Taylor and Elizabeth Kennedy are among the other fashion stars to get in touch with Bebe ahead of February's ceremony.


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Q: How to make a dropdown menu with jQuery I'm having trouble even getting started.
I want to have a drop down menu that disappears (except for the top box) when you aren't hovering over it.
That top box will appear with a blue background and white text, and an image.
When you hover, that box will turn into a yellow pointing arrow box, and all of the other elements will show, and they will be in black.
Everything will have an image (the now yellow top will keep the same image) and white text.
How do I go about this?
This is essentially what I have here - I'm assuming using jQuery to do this is best.

Setup Wizard

Language

Password

Bluetooth Devices

Network Config

Finish

A: you can accomplish this task by creating ul li in Jquery and for those effect use CSS.

 TEST

                    Setup Wizard

                    Language

                    Password

                    Bluetooth Devices

                    Network Config

                    Finish

A: There are a ton of tutorials on how to do this out there...I would recommend finding one that you like (style and behavior) and then looking at the jQuery, HTML, and CSS code to see how it works. Here are a couple of links to get you started:
http://css-tricks.com/simple-jquery-dropdowns/
http://www.1stwebdesigner.com/css/38-jquery-and-css-drop-down-multi-level-menu-solutions/

redpajama_set_name: RedPajamaStackExchange