% style file
\def\geqsim{\lower.73ex\hbox{$\sim$}\llap{\raise.4ex\hbox{$>$}}$\,$}
\def\leqsim{\lower.73ex\hbox{$\sim$}\llap{\raise.4ex\Shbox{$<$}}$\,$}
\newcommand{\fsl}[1]{\ensuremath{\mathrlap{\!\not{}}#1}}
% \fsl{<symbol>}\newcommand{\ov}{\overline}
\newcommand{\bos}{\boldsymbol}
\newcommand{\tbf}{\textbf}
\newcommand{\tit}{\textit}
\newcommand{\mcl}{\mathcal}
\newcommand{\mbf}{\mathbf}
\newcommand{\barr}{\begin{array}}
\newcommand{\earr}{\end{array}}
\newcommand{\bean}{\begin{eqnarray*}}
\newcommand{\eean}{\end{eqnarray*}}
\newcommand{\bei}{\begin{itemize}}
\newcommand{\eei}{\end{itemize}}
\newcommand{\ben}{\begin{enumeration}}
\newcommand{\een}{\end{enumeration}}
\newcommand{\tsc}{\textsc}
\newcommand{\la}{\langle}
\newcommand{\ra}{\rangle}
\newcommand{\lt}{\left}
\newcommand{\rt}{\right}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sign}{sign}
\newcommand{\grad}{\nabla}
\newcommand{\ing}{\includegraphics}
\newcommand{\ddx}{\frac{d}{dx}}
\newcommand{\bex}{\begin{example}}
\newcommand{\eex}{\end{example}}
\newcommand{\besp}{\begin{split}}
\newcommand{\ensp}{\end{split}}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\newcommand{\noi}{\noindent}
\newcommand{\ix}{\index}
\newcommand{\gam}{\gamma}%{\b}{\beta},{\d}{\delta},{\s}{\sigma}
\newcommand{\sDelta}{{\small{\Delta}}}
\newcommand{\lam}{\lambda}
\newcommand{\w}{\wedge}
\newcommand{\z}{\zeta}
\newcommand{\thet}{\theta}
\newcommand{\ro}{\rho}
\newcommand{\ta}{\tau}
\newcommand{\om}{\omega}
\newcommand{\boa}{\bos{\a}}
%\newcommand{\box}{\bos{x}}
\newcommand{\pr}{\prime}
\newcommand{\by}{\times}
\newcommand{\dagg}{\dagger}
%\newcommand{\ol}{\overline}
\newcommand{\ul}{\underline}
\newcommand{\evec}{eigenvector }
\newcommand{\evecs}{eigenvectors }
\newcommand{\eval}{eigenvalue }
\newcommand{\evals}{eigenvalues }
\newcommand{\esta}{eigenstate }
\newcommand{\estas}{eigenstates }
\newcommand{\tsl}{\textsl}
\newcommand{\mrm}{\mathrm}
\newcommand{\mbb}{\mathbb}
\newcommand{\msf}{\mathsf}
\newcommand{\re}{\mathrm{Re}}
\newcommand{\im}{\mathrm{Im}}
\newcommand{\leqn}{\lefteqn}
\newcommand{\btab}{\begin{tabular}}
\newcommand{\etab}{\end{tabular}}
\newcommand{\bpm}{\begin{pmatrix}}
\newcommand{\epm}{\end{pmatrix}}
\newcommand{\bbm}{\begin{bmatrix}}
\newcommand{\ebm}{\end{bmatrix}}
\newcommand{\bit}{\begin{itemize}}
\newcommand{\eit}{\end{itemize}}
\newcommand{\bct}{\begin{center}}
\newcommand{\ect}{\end{center}}
\newcommand{\ana}{analytic }
\newcommand{\ii}{_{-\infty}^\infty}
\newcommand{\oi}{_0^\infty}
\newcommand{\rb}{\bos{]}}
\newcommand{\lb}{\bos{[}}
\newcommand{\bes}{\begin{split}}
\newcommand{\ens}{\end{split}}
\newcommand{\pa}{\parallel}
\newcommand{\erf}{\mbox{erf}\,}
\newcommand{\erfc}{\mbox{erfc}\,}
\newcommand{\rar}{\rightarrow}
\newcommand{\qand}{\quad \mbox{and} \quad}
\newcommand{\qor}{\quad \mbox{or} \quad}
\newcommand{\ph}{\phantom}
\newcommand{\bigtranspose}
{{\mbox{${}^{\footnotesize\textsf{T}}$}}}
\newcommand{\transpose}
{{\mbox{${}^{\scriptsize{\textsf{T}}}$}}}
\newcommand{\transpos}
{{\mbox{${\scriptsize\textsf{T}}$}}}
\definecolor{navyblue}{rgb}{.05,0,.55}
\newcommand{\tcr}[1]{\textcolor{red}{#1}}
\newcommand{\tcb}[1]{\textcolor{blue}{#1}}
\newcommand{\tcnb}[1]{\textcolor{navyblue}{#1}}
\newcommand{\tcg}[1]{\textcolor{green}{#1}}
\newcommand{\tcy}[1]{\textcolor{yellow}{#1}}
\newcommand{\tcc}[1]{\textcolor{cyan}{#1}}
\newcommand{\tcm}[1]{\textcolor{magenta}{#1}}
\newcommand{\tcx}[1]{\textcolor{black}{#1}}
\newcommand{\ixx}[1]{\index{#1}\noindent}
\def\lsim{\:\raisebox{-.6ex}{$\stackrel{<}{\sim}$}\:}
\def\gsim{\:\raisebox{-.6ex}{$\stackrel{>}{\sim}$}\:}
\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\beqs{\begin{equation*}}
\def\eeqs{\end{equation*}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\ba{\begin{array}}
\def\ea{\end{array}}
\def\beas{\begin{eqnarray*}}
\def\eeas{\end{eqnarray*}}
\def\bq{\begin{quote}}
\def\eq{\end{quote}}
\def\p{\partial}
\def\a{\alpha}
\def\da{{\dot a}}
\def\ga{{(a)}}
\def\gb{{(b)}}
\def\gc{{(c)}}
\def\gab{{(ab)}}
\def\gac{{(ac)}}
\def\gi{{(i)}}
\def\gj{{(j)}}
\def\gk{{(k)}}
\def\gij{{(ij)}}
\def\gik{{(ik)}}
\def\b{\beta}
\def\db{{\dot b}}
\def\c{\gamma}
\def\dc{{\dot c}}
\def\d{\delta}
\def\dd{\dot{ d}}
\def\e{\varepsilon}
\def\ep{\epsilon}
\def\l{\lambda}
\def\bl{\bar\lambda}
\def\th{\theta}
\def\bth{\bar\theta}
\def\de{{\dot e}}
\def\be{{\bar {\e}}}
\def\s{\sigma}
\def\bs{{\bar {\s}}}
\def\df{\dot f}
\def\dg{\dot g}
\def\dh{\dot h}
\def\x{\xi}
\def\bx{\bar {\xi}}
\def\bz{\bar {z}}
\def\nn{\nonumber}
\def\o{\overline}
\def\dgr{\dagger}
\def\tr{{\rm Tr}}
\def\hc{{\rm h.c.}}
\def\t{\tilde}
\def\g{\grave}
\def\Tr{{\rm Tr}}
\def\half{\frac{1}{2}}
%\def\thalf{\textstyle{\frac{1}{2}}}
\def\thalf{ {\textstyle{ \frac{1}{2} }} }
\def\shalf{{\scriptstyle{\frac{1}{2}}}}
\def\sshalf{{\scriptscriptstyle{\frac{1}{2}}}}
\def\third{\frac{1}{3}}
\def\tthird{ {\textstyle{ \frac{1}{3} }} } 
\def\fourth{\frac{1}{4}}
\def\tfourth{ {\textstyle{ \frac{1}{4} }} } 
\def\fifth{\frac{1}{5}}
\def\sixth{\frac{1}{6}}
\def\seventh{\frac{1}{7}}
\def\eighth{\frac{1}{8}}
\def\ihalf{{\frac{i}{2}}}
\def\sqr2{\sqrt{2}}
\def\rhalf{\frac{1}{\sqrt{2}}}
\def\irhalf{\frac{i}{\sqrt{2}}}
\def\dcx{d^3\!x}
\def\dcy{d^3\!y}
\def\dcp{d^3\!p}
\def\dck{d^3\!k}
\def\vp{\varphi}
\def\cA{\mathcal A}
\def\cD{\mathcal D}
\def\cL{\mathcal L}
\def\cM{\mathcal M}
\def\cV{\mathcal V}
\def\G{Grassmann }
\def\qm{quantum mechanics }
\def\qmp{quantum mechanics}
\def\susy{supersymmetry }
\def\Susy{Supersymmetry }
\def\susyc{supersymmetric }
\def\susyp{supersymmetry}
\def\sf{superfield }
\def\sfs{superfields }
\def\sfp{superfield}
\def\sfsp{superfields}
\def\and{\quad {\hbox \mathrm{and}} \quad}
\def\for{\quad {\hbox \mathrm{for}} \quad}
\def\as{\quad {\hbox \mathrm{as}} \quad}
\def\whence{\quad {\hbox \mathrm{whence}} \quad}
\def\gappeq{\mathrel{\rlap {\raise.5ex\hbox{$>$}}
{\lower.5ex\hbox{$\sim$}}}}
\def\lappeq{\mathrel{\rlap{\raise.5ex\hbox{$<$}}
{\lower.5ex\hbox{$\sim$}}}}
