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"}]

$\phi^3$ theory

Tree level 1-loop level
  Renormalization ($\textrm{MS}, \overline{\textrm{MS}}$)

$\phi^4$ theory

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

Quantum Electrodynamics (QED)

Tree level 1-loop level 2-loop level
$e^+ e^- \to e^+ e^-$ $e^+ e^- \to e^+ e^-$ v.1 $e^- \to e^-$
$e^+ e^- \to \gamma \gamma$ $e^- \to e^-$ $\gamma \to \gamma$
$e^+ e^- \to \mu^+ \mu^-$ $e^- \to \gamma e^-$  
$e^- e^- \to e^- e^-$ $\gamma$  
$e^- \gamma \to e^- \gamma$ $\gamma \to \gamma$  
$e^- \mu^+ \to e^- \mu^+$ $\gamma \to \gamma \gamma$  
$\gamma \to \mu^+ \mu^-$ $\gamma \to \gamma \gamma \gamma \gamma$  
  $e^+ e^- \to \mu^+ \mu^-$ v.1  
  $\pi \to \gamma \gamma$  
  Renormalization ($\textrm{MS}, \overline{\textrm{MS}}$)  
  $e^+ e^- \to e^+ e^-$ v.2  
  $e^+ e^- \to \mu^+ \mu^-$ v.2  
  $\pi \to \gamma \gamma$  

Quantum chromodynamics (QCD)

Tree level 1-loop level 2-loop level
$e^+ e^- \to q \bar{q}$ $u_g \to u_g$ $u_g \to u_g$ v.1
$\gamma g \to q \bar{q}$ $u_g g \to u_g$ $u_g \to u_g$ v.2
$\gamma \to q \bar{q}$ $g \to g$ $g \to g$
$\gamma \to q \bar{q} g$ $g \to g$ (background field gauge)  
$g g \to g g$ $g \to g g$  
$g g\to q \bar{q}$ $q \to q$  
$\mu^+ \mu^- \to q \bar{q}$ Renormalization ($\textrm{MS}, \overline{\textrm{MS}}$)  
$q \gamma \to g q$ Renormalization ($\textrm{MS}, \overline{\textrm{MS}}$), massless quarks  
$q g \to q g$ v.1    
$q_i \bar{q}_i \to q_i \bar{q}_i$    
$q_i \bar{q}_i \to q_j \bar{q}_j$    
$q_i q_i \to q_i q_i$    
$q_i \bar{q}_j \to q_i \bar{q}_j$    
$q_i q_j \to q_i q_j$    
$q \bar{q} \to e^+ e^-$    
$q \bar{q} \to \gamma \gamma$    
$q \bar{q} \to \gamma g$    
$q \bar{q} \to g g$    
$q \bar{q} \to \mu^+ \mu^-$    
Soft function $\gamma \to q \bar{q} $    
$q g \to q g$ v.2    
$q \bar{q} \to g g$ v.2    

Electroweak theory (EW)

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

Yukawa theory

Tree level 1-loop level
  Renormalization ($\textrm{MS}, \overline{\textrm{MS}}$)

Minimal Supersymmetric Standard Model (MSSM)

Tree level 1-loop level
\(\tilde{\nu}_e e^- \to \tilde{\nu}_e e^-\)  

Topology identification and minimization

1-loop level 2-loop level 3-loop level
  \(B_c \to \eta_c\)  

FeynRules models for FeynArts

Models
\(\phi^3\)
\(\phi^4\)
\(\phi^3 + \phi^4\)
Euler-Heisenberg EFT
QED
QCD
QCD in background field gauge
Standard Model
Yukawa

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.

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Formalities

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