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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /fonts/feyn/exercise-font.tex
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+\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}