diff options
author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /fonts/feyn/exercise-font.tex |
Initial commit
Diffstat (limited to 'fonts/feyn/exercise-font.tex')
-rw-r--r-- | fonts/feyn/exercise-font.tex | 290 |
1 files changed, 290 insertions, 0 deletions
diff --git a/fonts/feyn/exercise-font.tex b/fonts/feyn/exercise-font.tex new file mode 100644 index 0000000000..928d1cd7f6 --- /dev/null +++ b/fonts/feyn/exercise-font.tex @@ -0,0 +1,290 @@ +\documentclass[10pt]{article} + +\usepackage{feyn} + +\expandafter\ifx\csname useextended\endcsname\relax + \let\ff\feyn + \let\dd\Diagram +\else + \let\ff\FEYN + \let\dd\DIAGRAM +\fi + +\makeatletter +\def\refptcirc{\lower\feyn@maxis \hbox to 0pt{\hss$\circ$\hss}} +\makeatother +\let\\\cr + +\parindent=0pt + +\begin{document} + +Alphabetically: + +\halign{#\hfil\quad&$\refptcirc\ff{#}$\cr +a & a \\ +b & b \\ +c & c \\ +d & d \\ +e & e \\ +f & f \\ +g & g \\ +h & h \\ +i & i \\ +j & j \\ +k & k \\ +l & l \\ +m & m \\ +n & n \\ +o & o \\ +p & p \\ +q & q \\ +r & r \\ +s & s \\ +t & t \\ +u & u \\ +v & v \\ +w & w \\ +x & x \\ +y & y \\ +z & z \\ +} + +\vskip 2cm + +\newdimen\feynmod +\makeatletter +\feynmod=\feyn@module +Dimensions: +Feyn module: \the\feyn@module, +math-axis: \the\feyn@maxis. +\makeatother + +\newpage + +With ligatures: +\def\T{\tracingmacros=2 \tracingcommands=2 } + +\halign{&\vrule width 0pt height 1\feynmod #\hfil\quad&$\refptcirc\ff{#}$\qquad \cr +a & a & aA & aA & aV & aV\\ +f & f & fA & fA & fV & \momentum{fV}{pk} \\ +fu & fu & fuA & fuA & fuV & \momentum{fuV}{pk} \\ +fd & fd & fdA & fdA & fdV & \momentum{fdV}{pk} \\ +fv & fv & fvA & fvA & fvV & \momentum{fvV}{pk} \\ +fl & fl & flA & flA & flV & \momentum{flV}{pk} \\ +flu & flu & fluA & fluA & fluV & \momentum{fluV}{pk} \\ +flS& flS & flSA & flSA & flSV & \momentum{flSV}{pk} \\ +flSu& flSu & flSuA & flSuA & flSuV & \momentum{flSuV}{pk} \\ +flo & flo & floA & floA & floV & \momentum{floV}{pk} \\ +fs & |fs| \\ +fs0 & |fs0| \\ +g & g & gA & gA & gV & \momentum{gV}{pk} \\ +gu & gu & guA & guA & guV & \momentum{guV}{pk} \\ +gd & gd & gdA & gdA & gdV & \momentum{gdV}{pk} \\ +gv & gv & gvA & gvA & gvV & \momentum{gvV}{pk} \\ +g1 & g1 & g1A & g1A & g1V & \momentum{g1V}{pk} \\ +g2 & g2 & g2A & g2A & g2V & \momentum{g2V}{pk} \\ +g3 & g3 & g3A & g3A & g3V & \momentum{g3V}{pk} \\ +g4 & g4 & g4A & g4A & g4V & \momentum{g4V}{pk} \\ +gl & gl & glA & glA & glV & \momentum{glV}{pk} \\ +glu & glu & gluA & gluA & gluV & \momentum{gluV}{pk} \\ +glB & glB \\ +glS & glS \\ +m & m & mA & mA & mV & \momentum{mV}{pk} \\ +ms & ms & ms & \momentum{ms}{pk} \\ +h & h & hA & hA & hV & \momentum{hV}{pk} \\ +hu & hu & huA & huA & huV & \momentum{huV}{pk} \\ +hd & hd & hdA & hdA & hdV & \momentum{hdV}{pk} \\ +hs & hs & hs & \momentum{hs}{pk} \\ +hl & hl & hlA & hlA & hlV & \momentum{hlV}{pk} \\ +hlu & hlu & hluA & hluA & hluV & \momentum{hluV}{pk} \\ +x & x & x & \momentum{x}{pk} \\ +p & p & P & \momentum{P}{pk} \\ +c & c & c & \momentum{c}{pk} \\ +a & a & A & A \\ +} + +\newpage + +\def\twice#1{#1 & #1 } + +\halign{&#\hfil\quad&$\refptcirc\ff{#}$\qquad\cr +\twice{fs f gl gv f fs}&vertical gluon doesn't meet -- OK\\ +\twice{fs f glA gv f fs}\\ +\twice{fs fA glA gvV f fs}\\ +\twice{fs fA g1A gvV g2V fA fs}&vertical gluon meets\\ +\twice{msmA g1gvg2 msxf}&and here\\ +} + +\vskip10ex + +\textbf{More complicated diagrams} + +Fermion, gluon and ghost loop: +\[ +\Diagram{\hline&fl flu \\ +\hline +fsf g1 f&f g2 ffs \\ +\hline} +\quad +\Diagram{\hline&gl glu\\ +fsf g1 f&f g2 ffs \\} +\quad +\Diagram{\hline&hlA hluV \\ +fsf g1 f&f g2 ffs \\} +\] + +\textbf{Annotations:} + +a: $\ff{!f1\momentum{fA}2}$ (arrow rightward) + +b: $\ff{f !{gluV}k f}$ (arrow leftward) +\vskip 10ex + +c: $\ff{f !{g1A}1 \momentum{g2V}2 \momentum{g3A}3 \momentum{g4V}4 f}$ +(arrows are 1=right, 2=left, 3=right, 4=left) +\vskip 10ex + +d: $\ff{\momentum{gl}a\momentum{gluV}b}$ +(arrow leftwards) +\vskip 10ex + +e: $\ff{fs f \momentum{flA}{pk} \momentum{fluV}{pk} f fs}$ +(arrows right then left) +\vskip 10ex + +f: $\ff{fs f \momentum{flSA}{pk} \momentum{flSuV}{pk} f fs}$ +\vskip 10ex + +g: $\ff{fflof\momentum{floV}{p}f\momentum{floA}{p}f}$ + +%error: $\ff{\momentum{x}x}$ + +\newpage + +Vertex Feynman diagram: +\[ +\dd{\vertexlabel^a \\ + fd \\ +& g\vertexlabel_{\mu,c} \\ +\vertexlabel_b fu \\ +} += +\dd{\vertexlabel^a \\ + fdA \\ +& gA\vertexlabel_{\mu,c} \\ +\vertexlabel_b fuV \\ +} += +\dd{\momentum{fdA}a\\ + & \vertexlabel_{\gamma_\mu} \momentum{gA}{\mu,c} \\ +\momentum{fuV}b +} += +ig\gamma_\mu (T^c)_{ab} +\] + +Use of the `belowl' macro: +\[ +\feyn{fd \belowl{fu} g + + + fA guA \belowl{fdA} +} += +\FEYN{fd \belowl{fu} g + + + fA guA \belowl{fdA} +} +\] + +Two-loop diagram: +\[ +\ff{ff gl ff} +\to +\ff{ff\bigbosonloopA\smallbosonloopV ff} += +\ff{!{fA}p f!{glBV}k !{glSA}l a\vertexlabel_{p+k-l} ff} +\] + +Bremsstrahlung: +\[ + \dd{ & x \\ + & ![ulft]{gvV}{q=p'+k-p} & !{guA}k \\ + ![bot]{fA}p & ![bot]{fA}{p'+k} & ![lrt]{fA}{p'} \\ + } + + + \dd{ & !{guA}k \\ + !{fA}p & fs ![bot]{fA}{p-k} & !{fA}{p'} \\ + & & ![lrt]{gvA}{q=p'+k-p} \\ + & & x\\ + } +\] + +OPE: +\def\bracket#1{\langle #1 \rangle} +\begin{eqnarray*} +-i\Sigma_{\mathrm{ope}} &=& + \left[\ff{faf + fsfglffs + + \cdots} \right] 1 \\ + && \quad{}+ + \left[ \ff{ fxfs0glfs0xf + + \cdots} \right] + \bracket{\overline\psi M \psi} \\ + && \quad{}+ \left[ + \dd{ &x &x \\ + &gv &gv \\ + fs &fs &fs \\} + \cdots + \right] + \bracket{G_{\mu\nu}^a G_{\mu\nu}^a}\\ +\end{eqnarray*} + +Complete vertex: +\begin{eqnarray*} +\ff{fcf} &=& \ff{faf + fpf + fpfpf + \cdots} \\ + &=& \sum_{n=0}^\infty \ff{fA ( pfA)}^n \\ + &=& \ff{\frac{fA}{1-(pfA)}}. +\end{eqnarray*} + +\iffalse +\halign{&#\hfil\quad&$\refptcirc\ff{#}$ \cr +a & a \\ +c & c \\ +f & f \\ +F & F \\ +fs & fs \\ +fl & fl \\ +fu & fu \\ +fd & fd \\ +fv & fv \\ +f0 & f0 \\ +fs0 & fs0 \\ +g & g \\ +G & G \\ +gl & gl \\ +glu & glu \\ +$\backslash$ smallbosonloop & \smallbosonloop \\ +$\backslash$ bigbosonloop & \bigbosonloop \\ +gu & gu \\ +gd & gd \\ +gv & gv \\ +gvs & gvs \\ +gvb & gvb \\ +h & h \\ +hs & hs \\ +hu & hu \\ +hd & hd \\ +k & k \\ +l & l \\ +m & m \\ +ms & ms \\ +n & n \\ +o & o \\ +p & p \\ +x & x \\ +w & w \\ +%000 & \arrow000\\ +%00 45 & \arrow00{45}\\ +} +\fi + +\end{document} |