%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % MYPHYX for TEX Version 2.9 -- created 12/15/88 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \def\MYHEAD{\setbox0=\vtop{\baselineskip=10pt \ialign{\eightrm ##\hfil\cr \slacbin\cr P.~O.~Box 4349\cr Stanford, CA 94309\cropen{1\jot} (415) 926--4423\cr SHARON at SLACVM\cr}}% \setbox2=\hbox{\caps Stanford Linear Accelerator Center}% \hrule height 0pt \kern -0.5in \vbox to 0pt{\vss\centerline{\seventeenrm STANFORD UNIVERSITY}} \vbox{} \medskip \line{\hbox to 0.7\hsize{\hss \lower 10pt \box2 \hfill }\hfil \hbox to 0.25\hsize{\box0 \hfil }}\medskip } \def\myletter{\let\letterhead=\MYHEAD \letter} \def\binno{81} \def\slacext{2266} \def\half{\hbox{${1\over 2}\,$}} \def\etal{{\it et al.}} \def\bar#1{\overline{#1}} \def\kbar{{\mathchar'26\mskip-9muk}} \def\pbar{{\rlap/p}} \def\ubar{\bar{u}} \def\dbar{\bar{d}} \def\str{\penalty-10000\hfilneg\ } % line break with right adjust \def\Str{\penalty-10000\hfilneg\ } % line break with right adjust \def\nostr{\hfill\penalty-10000\ } % line break with ragged right \let\brk=\nextline \def\|{\vrule height 16pt depth 6 pt} \def\ZZ{\hbox{$\not\kern0.15em\not\kern-0.21em\lower0.2em \vbox{\hrule width 0.52em height 0.06em depth 0pt} \kern-0.50em\raise0.7em \vbox{\hrule width 0.52em height 0.06em depth 0pt}$}} \def\frac#1/#2{\leavevmode\kern.1em\raise.5ex\hbox{\the\scriptfont0 #1}\kern-.1em/\kern-.15em\lower.25ex\hbox{\the\scriptfont0 #2}} % \frac3/4 gives you a very nice 3/4 - slanted. \def\IR{{$\rm I\!R$}} \def\lozenge{\boxit{\hbox to 1.5pt{ \vrule height 1pt width 0pt \hfill}}} \def\Buildrel#1\under#2{\mathrel{\mathop{#2}\limits_{#1}}} \def\simZ{{\Buildrel \sim \under Z}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This macro inserts pictures (and, more generally, \vbox es) neatly % into the MIDDLE of a paragraph. % --- #1 should be a \vbox --- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\pix#1{\vadjust{\vbox{\kern 1.0cm #1 \kern 1.0cm}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % These macros insert (\vbox es) using respectively \topinsert and % \pageinsert. Since these macros put you into vertical mode, % they should only be called BETWEEN paragraphs. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\tpix#1{\topinsert #1 \endinsert} \def\ppix#1{\pageinsert #1 \endinsert} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % To define a \vbox for an inserted figure, use the following command: % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \Picture\CompEP\height=4.125in \width=\hsize\caption{\narrower % The caption goes here.} % \savepicture\FigureOne % (\Picture calls \FIG and assigns the figure the caption % indicated and the figure number \CompEP. It also % creates a \vbox of the right size for a picture % of the indicated height, and \savepicture assigns this % to the macro \FigureOne.) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % TWO LINE MACRO (used in tables) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\twoline#1:#2#3{\vtop{\hbox to #1{\hss \strut #2 \hss} \hbox to #1{\hss \strut #3 \hss}}} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Three nice dots left to right moving upward. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \def\mddots{\mathinner{\mskip1mu\raise1pt\hbox{.}\mskip2mu \raise4pt\hbox{.}\mskip2mu\raise7pt\vbox{\kern7pt\hbox{.}}\mskip1mu}} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \clock returns time in hours:minutes on a 24 hour basis % check \fullclock too % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \newcount\timecount \newcount\hours \newcount\minutes \newcount\temp \newcount\pmhours \hours = \time \divide\hours by 60 \temp = \hours \multiply\temp by 60 \minutes = \time \advance\minutes by -\temp \def\hour{\the\hours} \def\minute{\ifnum\minutes<10 0\the\minutes \else\the\minutes\fi} \def\clock{ \ifnum\hours=0 12:\minute\ AM \else\ifnum\hours<12 \hour:\minute\ AM \else\ifnum\hours=12 12:\minute\ PM \else\ifnum\hours>12 \pmhours=\hours \advance\pmhours by -12 \the\pmhours:\minute\ PM \fi \fi \fi \fi } \def\fullclock{\hour:\minute} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \draft causes the symbolic names of equations to be printed % alongside the equation numbers % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \let\eqnameold=\eqname \def\draft{\def\eqname##1{\eqnameold##1:{\tt\string##1}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Letter with no letterhead % insert \blankheads after \letters % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\blankheads{\let\letterhead=\blankletterhead \lettertopskip=7pt plus 3pt} \def\blankletterhead{\hrule height 0pt \vskip 1.3in} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % this gives you a boldface character in math mode. % $\bold\beta$ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\bold#1{\setbox0=\hbox{$#1$}% \kern-.025em\copy0\kern-\wd0 \kern.05em\copy0\kern-\wd0 \kern-.025em\raise.0433em\box0 } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Definition for a slash over a letter % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % from M. Peskin \def\dslash{\not{\hbox{\kern-2pt $\partial$}}} \def\Dslash{\not{\hbox{\kern-4pt $D$}}} \def\Qslash{\not{\hbox{\kern-4pt $Q$}}} \def\pslash{\not{\hbox{\kern-2.3pt $p$}}} \def\kslash{\not{\hbox{\kern-2.3pt $k$}}} \def\qslash{\not{\hbox{\kern-2.3pt $q$}}} % % \newtoks\slashfraction \slashfraction={.13} \def\slash#1{\setbox0\hbox{$ #1 $} \setbox0\hbox to \the\slashfraction\wd0{\hss \box0}/\box0 } % EXAMPLE OF HOW TO USE IT % $\slash D$ % {\slashfraction={.075} $\slash{\cal A}$} % $\slash B$ % $\slash a$ % {\slashfraction={.09} $\slash p$} % $\slash q$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % this gives you \leftrightarrow over \slash\partial % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\leftrightarrowfill{$\mathord-\mkern-6mu% \cleaders\hbox{$\mkern-2mu\mathord-\mkern-2mu$}\hfill \mkern-6mu\mathord\leftrightarrow$} \def\overlrarrow#1{\vbox{\ialign{##\crcr \leftrightarrowfill\crcr\noalign{\kern-1pt\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} % $$ \overlrarrow{\slash\partial} $$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This is a macro written by Marvin which makes Young tableaux: % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\yboxit#1#2{\vbox{\hrule height #1 \hbox{\vrule width #1 \vbox{#2}\vrule width #1 }\hrule height #1 }} \def\fillbox#1{\hbox to #1{\vbox to #1{\vfil}\hfil}} \def\ybox{\yboxit{0.4pt}{\fillbox{8pt}}\hskip-0.4pt} \def\nbox{\yboxit{0pt}{\fillbox{8pt}}} \def\tableaux#1{\vcenter{\offinterlineskip \halign{&\tabskip 0pt##\cr #1}}} \def\cry{\cropen{-0.4pt}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % An example of the use of \tableaux is: % $$ X = \tableaux{\ybox & \ybox & \ybox \cry % \ybox & \ybox & \nbox \cry % \ybox & \nbox & \nbox \cry} $$ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % by M. Peskin % These macros make 4- and 5-pt skeleton diagrams % with labelled endpoints and internal lines. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\fourptfcn#1#2#3#4#5{ \matrix{#1\cr\cr#2\cr} \hbox{$ \Bigg\rangle \kern -2.5pt {\phantom{whichcan}\over {\textstyle \downabit #5} } \kern-2.5pt \Bigg\langle$} \matrix{#3\cr\cr#4\cr} } \def\fiveptfcn#1#2#3#4#5#6#7{ \matrix{#1\cr\cr#2\cr} \hbox{$ \Bigg\rangle \kern -2.5pt {{\pile} \lower 6pt\hbox{$\spire#5$} {\pile}\over \phantom{can}{\textstyle \downabit#6}\phantom{which} {\textstyle \downabit #7}\phantom{can}} \kern-2.5pt \Bigg\langle$} \matrix{#3\cr\cr#4\cr} } \def\spire#1{\matrix{#1\cr\Bigm|\cr}} \def\pile{\phantom{\matrix{1\cr2\cr3\cr}}} \def\downabit{\vphantom{\bigm|}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\unlock{\catcode`@=11} % This allows us to modify PLAIN macros. % \def\lock{\catcode`@=12} % at signs are no longer letters % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % These changes give you references on the line in brackets [3] % and in the reference list. [1] A. Einstein ... % % %\unlock %\def\step@ver#1{\rel@x \ifmmode #1\else \ifhmode % \roll@ver{$\ {} #1$ }\else {\setbox0=\hbox{${} #1$ }}\fi\fi } %\def\attach#1{\step@ver{\strut {\mkern 4mu #1} }} %\def\normalrefmark#1{\attach{ [ #1 ] }} %\def\NPrefmark#1{\step@ver{{\ [#1]}}} %\def\refitem#1{\r@fitem{[#1]}} %\lock %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %