FeynCalc manual (development version)

FCPermuteMomentaRules

FCPermuteMomentaRules[{p1, p2, ...}] returns a set of rules that contain all possible permutations of the momenta p1, p2, … . This can be useful when working with amplitudes that exhibit a symmetry in some or all of the final state momenta or when trying to find mappings between loop integrals from different topologies.

See also

Overview, FCReplaceMomenta.

Examples

FCPermuteMomentaRules[{p1, p2}] 
 
f[p1, p2] /. %

{{},{p1  p2,p2  p1}}\{\{\},\{\text{p1}\to \;\text{p2},\text{p2}\to \;\text{p1}\}\}

{f(p1,p2),f(p2,p1)}\{f(\text{p1},\text{p2}),f(\text{p2},\text{p1})\}

FCPermuteMomentaRules[{p1, p2, p3}] 
 
f[p1, p2, p3] /. % 
  
 

{{},{p1  p2,p2  p1},{p1  p3,p3  p1},{p2  p3,p3  p2},{p1  p2,p2  p3,p3  p1},{p1  p3,p2  p1,p3  p2}}\{\{\},\{\text{p1}\to \;\text{p2},\text{p2}\to \;\text{p1}\},\{\text{p1}\to \;\text{p3},\text{p3}\to \;\text{p1}\},\{\text{p2}\to \;\text{p3},\text{p3}\to \;\text{p2}\},\{\text{p1}\to \;\text{p2},\text{p2}\to \;\text{p3},\text{p3}\to \;\text{p1}\},\{\text{p1}\to \;\text{p3},\text{p2}\to \;\text{p1},\text{p3}\to \;\text{p2}\}\}

{f(p1,p2,p3),f(p2,p1,p3),f(p3,p2,p1),f(p1,p3,p2),f(p2,p3,p1),f(p3,p1,p2)}\{f(\text{p1},\text{p2},\text{p3}),f(\text{p2},\text{p1},\text{p3}),f(\text{p3},\text{p2},\text{p1}),f(\text{p1},\text{p3},\text{p2}),f(\text{p2},\text{p3},\text{p1}),f(\text{p3},\text{p1},\text{p2})\}