PairContract
is like Pair
, but with (local) contraction properties. The function fully supports the BMHV algebra and will expand momenta inside scalar products when it leads to simpler expressions.
PairContract
is an auxiliary function used in higher level FeynCalc functions that require fast contractions between multiple expressions, where Contract
would be too slow.
Overview, Contract, PairContract2, PairContract3.
[LorentzIndex[\[Mu]], Momentum[p]] Pair[LorentzIndex[\[Mu]], Momentum[q]]
Pair
% /. Pair -> PairContract
[LorentzIndex[\[Mu]], Momentum[p]] Pair[LorentzIndex[\[Nu]], Momentum[q]] Pair[LorentzIndex[\[Mu]], LorentzIndex[\[Nu]]]
Pair
% /. Pair -> PairContract
[LorentzIndex[\[Mu]], Momentum[p + q]] Pair[LorentzIndex[\[Mu]], Momentum[r + s]]
Pair
% /. Pair -> PairContract
[];
FCClearScalarProducts[p1, p2] = s2;
SP[p1, p3] = s3;
SP[SP[p1, p2 + p3]] /. Pair -> PairContract FCI