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