Example gallery · FeynCalc

Here we collect examples of interesting calculations from textbooks and papers that can be reproduced using FeynCalc. The HTML pages below were generated from example notebooks shipped with the current stable version of Feyncalc. If you have FeynCalc installed, these files are located in

FileNameJoin[{$UserBaseDirectory, "Applications", "FeynCalc", "Examples"}]

Quantum Electrodynamics (QED)

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	massive, massless, old	$\gamma \to \gamma$, $\ell \to \ell$, massless $\ell \to \ell$
$e^+ e^- \to e^+ e^-$	link	link
$e^+ e^- \to \mu^+ \mu^-$	link	link
$e^+ e^- \to \gamma \gamma$	link
$e^- \mu^+ \to e^- \mu^+$	link
$e^- \gamma \to e^- \gamma$	link
$e^- e^- \to e^- e^-$	link
$e^- \to \gamma e^-$	X	$g-2$
$\gamma$	X	Furry’s theorem
$\gamma \to \gamma \gamma$	X	Furry’s theorem
$\gamma \to \gamma \gamma \gamma \gamma$	X	Furry’s theorem
$\gamma \to \mu^+ \mu^-$	link
$\pi \to \gamma \gamma$	X	Axial anomaly

Quantum chromodynamics (QCD)

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	massive, massless, old massive, old massless	$g \to g$, $u_g \to u_g$, $q \to q$, massless $q \to q$, $q g \to q$
$g g \to H$	X		link
$g g \to H H$	X	link
$H \to g g$	X	link
$g \to g$	X	BG field gauge	link
$u_g \to u_g$	X		link
$g \to g g$	link
$e^+ e^- \to q \bar{q}$	link
$\gamma g \to q \bar{q}$	link
$\gamma \to q \bar{q}$	link
$\gamma \to q \bar{q} g$	link
$g g \to g g$	link
$g g\to q \bar{q}$	link
$\mu^+ \mu^- \to q \bar{q}$	link
$q \gamma \to g q$	link
$q g \to q g$	v1, v2
$q_i \bar{q}_i \to q_i \bar{q}_i$	link
$q_i \bar{q}_i \to q_j \bar{q}_j$	link
$q_i q_i \to q_i q_i$	link
$q_i \bar{q}_j \to q_i \bar{q}_j$	link
$q_i q_j \to q_i q_j$	link
$q \bar{q} \to e^+ e^-$	link
$q \bar{q} \to \gamma \gamma$	link
$q \bar{q} \to \gamma g$	link
$q \bar{q} \to g g$	v1, v2
$q \bar{q} \to \mu^+ \mu^-$	link
Soft function $\gamma \to q\bar{q}$	link

Electroweak theory (EW)

Process	Tree level	1-loop level	2-loop level
$q \bar{q} \to Z^0 Z^0$	link
$H \to f \bar{f}$	link
$H \to W^+ W^-$	link
$H \to Z^0 Z^0$	link
$W \to q_i \bar{q}_j$	link
$Z \to f \bar{f}$	link
${\bar{\nu}}e e^- \to {\bar{\nu}}{\mu} \mu$	link
$\bar{\nu}_e e^- \to \bar{q}_u q_d$	link
$\bar{\nu}_e e^- \to W^+ W^-$	link
$\bar{\nu}_e e^- \to Z^0 Z^0$	link
$e^- \nu_{\mu} \to \mu \nu_{e}$	link
$\nu_l q_d \to l q_u$	link
$\bar{q}_d q_u \to \bar{\nu}_e \nu_e$	link
$\bar{q}_u q_d \to \bar{\nu}_e \nu_e$	link
$W^- \to e^- \bar{\nu}_e$	link
$\mu \to e^- {\bar{\nu}}_{e} \nu_{\mu}$	link
$t \to W^+ b$	link

$\phi^3$ theory

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	link

$\phi^4$ theory

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	link	$\phi \to \phi$, $\phi \phi \to \phi \phi$
$\phi \phi \to \phi \phi$		link

Scalar Yukawa theory

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	link

Pseudoscalar Yukawa theory

Process	Tree level	1-loop level	2-loop level
Renormalization ($\overline{\textrm{MS}}$)	X	link

Minimal Supersymmetric Standard Model (MSSM)

Process	Tree level	1-loop level	2-loop level
$\tilde{\nu}_e e^- \to \tilde{\nu}_e e^-$	link

Topology identification and minimization

Process	1-loop level	2-loop level	3-loop level
$B_c \to \eta_c$	X	link

Acknowledgement

To generate Markdown files out of FeynCalc notebooks we employed the M2MD package by Kuba Podkalicki. We thank the author for helpful advice on using the package in a proper way.