LC[m, n, r, s]
evaluates to 4-dimensional by virtue of applying FeynCalcInternal
.
LC[m,...][p, ...]
evaluates to 4-dimensional applying FeynCalcInternal
.
When some indices of a Levi-Civita-tensor are contracted with 4-vectors, FeynCalc suppresses explicit dummy indices by putting those vectors into the corresponding index slots. For example, (accessible via LC[][p1,p2,p3,p4]
) correspond to .
[\[Mu], \[Nu], \[Rho], \[Sigma]] LC
[\[Mu], \[Nu], \[Rho], \[Sigma]] // FCI // StandardForm
LC
(*Eps[LorentzIndex[\[Mu]], LorentzIndex[\[Nu]], LorentzIndex[\[Rho]], LorentzIndex[\[Sigma]]]*)
[\[Mu], \[Nu]][p, q] LC
[\[Mu], \[Nu]][p, q] // FCI // StandardForm
LC
(*Eps[LorentzIndex[\[Mu]], LorentzIndex[\[Nu]], Momentum[p], Momentum[q]]*)
[LC[\[Mu], \[Nu], \[Rho]][p] LC[\[Mu], \[Nu], \[Rho]][q]] Contract
[\[Mu], \[Nu], \[Rho], \[Sigma]] FV[Subscript[p, 1], \[Mu]] FV[Subscript[p, 2], \[Nu]] FV[Subscript[p, 3], \[Rho]] FV[Subscript[p, 4], \[Sigma]]
LC
[%] Contract