draft.tex

%%This is a very basic article template.
%%There is just one section and two subsections.
\documentclass[11pt,oldfontcommands]{memoir}

\include{header}
\pagenumbering{arabic}
\numberwithin{equation}{section}
%NEW COMMANDS



\newcommand{\sectionline}{%
  \nointerlineskip \vspace{\baselineskip}%
 \rule{0.5\linewidth}{.7pt}\hspace{\fill}%
  \par\nointerlineskip \vspace{\baselineskip}
}



\newcommand{\hC}{^{12}C^{5+} }
\newcommand{\hO}{^{16}O^{7+} }

\newcommand{\beqa}{\begin{eqnarray*} }
\newcommand{\eeqa}{\end{eqnarray*} }
\newcommand{\beq}{\begin{equation} }
\newcommand{\eeq}{\end{equation} }
\newcommand{\beqB}{\begin{equation*}}
\newcommand{\eeqB}{\end{equation*}}

\newcommand{\beqaL}{\begin{eqnarray} }
\newcommand{\eeqaL}{ \end{eqnarray} }
% macros used for consistency
\newcommand{\Psibar}{\bar{\Psi}}
\newcommand{\rapidity}{\phi}
\newcommand{\TensBi}{\Sigma} %(Tensor bilinear)

%nonrelativistic wave functions
\newcommand{\phis}{\phi_S}
\newcommand{\wnr}{\phi_S}
\newcommand{\wnrb}{\phi_S^\dagger}

%Temp command to make it easy to replace all those Ws in spin half QED work
\newcommand{\wx}{\phis}
\newcommand{\wxd}{\phis^\dagger}

%nonrelativistic fields
\newcommand{\fnr}{\psi}
\newcommand{\fnrb}{\psi^\dagger}

%relativistic fields
\newcommand{\fr}{\Psi}
\newcommand{\frb}{\bar{\Psi} }

%spinors u, ubar
\newcommand{\sr}{u}
\newcommand{\srb}{\bar{u}}

%General spin bispinor:
\newcommand{\Psig}{\Psi}
\newcommand{\Psigbar}{\bar{\Psi}}


\newcommand{\smalldot}{\cdot}
%from dirac_redo.tex
\newcommand{\sigdot}[1]{ \gv{\sigma} \hspace{-2pt} \cdot \hspace{-2pt} \v{#1} \,}
\newcommand{\sigdotg}[1]{ \gv{\sigma} \hspace{-2pt} \cdot \hspace{-2pt} \gv{#1} \,}
\newcommand{\explus}{(\sigdotg{\pi} - i\mu' \sigdot{E} )}
\newcommand{\exminus}{(\sigdotg{\pi} + i\mu' \sigdot{E} )}

\newcommand{\gradE}{\grad}

%Macro for weight matrix
\newcommand{\weight}{\Omega}


%matrix/vector/spinor shorthands
\newcommand{\spinor}[2]{ \begin{pmatrix} #1 \\ #2 \end{pmatrix} }
\newcommand{\Mblock}[4]{\begin{pmatrix} #1 & #2 \\ #3 & #4 \end{pmatrix} }

\newcommand{\Sb}{\overline{S}}

\newcommand{\A}{\epsilon}
\newcommand{\Adag}{\epsilon'}
\newcommand{\W}{\omega}
\newcommand{\Wdag}{\omega^*}

%-------
%macros for different term labels
%-------

%g dependent part of one photon calc
\newcommand{\Mg}{M_g}
%other part of one-photon calc
\newcommand{\Mq}{M_q}
%two-photon vertex contribution to Compton
\newcommand{\Mcontact}{M_{\text{contact}}}
\newcommand{\Mtrees}{M_{\text{trees} }}


\newcommand{\VertexEq}[2]{ \mbox{
\begin{minipage}{1.6in}
   \includegraphics[scale=0.8]{eps/#1} 
\end{minipage}
{ \large $	=	\hspace{2em} 	\large{#2} $ }
} }



% shortcuts for the binspinors represented as vectors.  Used in spin-half.tex, imported from uv_bilinears.tex
\newcommand{\uvec}[1]{ \begin{pmatrix} \varphi \\ \frac{\sigdot{#1}}{2m} \varphi \end{pmatrix} }
\newcommand{\vvec}[1]{ \begin{pmatrix} \frac{\sigdot{#1}}{2m} \chi \\ \chi \end{pmatrix} }
\newcommand{\udaggervec}[1]{ \begin{pmatrix} \varphi^\dagger & \frac{\sigdot{#1}}{2m} \varphi^\dagger \end{pmatrix} }
\newcommand{\vdaggervec}[1]{ \begin{pmatrix} \frac{\sigdot{#1}}{2m}  \chi^\dagger & \chi^\dagger \end{pmatrix} }

\newcommand{\ubar}{\bar{u}}
\newcommand{\vbar}{\bar{v}}%


%% Commands from spin1-diagrams
\newcommand{\snote}[1]{}
\newcommand{\qp}{q^{(+)}{}}
\newcommand{\qm}{q^{(-)}{}}
 \newcommand{\E}[1]{ \sqrt{ m^2 + \v{#1}^2 } }
% % \newcommand{\E}[1]{ E_{#1} }
 \newcommand{\diracdelta}[1]{ \delta^{(3)}(#1) }
 \newcommand{\epin}[1]{ \epsilon_{#1}(p) }
 \newcommand{\epout}[1]{ \epsilon^*_{#1}(p') }
\newcommand{\omin}[1]{ \omega_{#1}(p) }
 \newcommand{\omout}[1]{ \omega^*_{#1}(p') }

 

\usepackage{setspace}
\DoubleSpacing

\setlength{\TPHorizModule}{1in}\setlength{\TPVertModule}{1in}

\title{Universal Binding and Recoil Corrections to Bound State $g$-Factors}
\author{Timothy J. S. Martin}


\begin{document}
 
\maketitle

\frontmatter*
\include{cover}
\include{abstract}
 \tableofcontents
\include{intro2}

\mainmatter

\include{NRQED-review}
\include{Spin-half}
\include{SpinOne-Equations}
\include{Spin1-Diagrams}
%\include{NRQED}
\include{GeneralSpin}
\include{breit}


\include{Conclusions}
%\include{pert}
\include{appendix}

\backmatter
\bibliographystyle{plain}
\bibliography{refs}

\end{document}