GAE[mu]
can be used as input for a D-4
-dimensional \gamma^{\mu }and is transformed into DiracGamma[LorentzIndex[mu, D-4], D-4]
by FeynCalcInternal
(FCI
).
GAE[mu, nu , ...]
is a short form for GAE[mu].GAE[nu] ...
.
Overview, DiracGamma, GA, GS, GAD.
[\[Mu]] GAE
\hat{\gamma }^{\mu }
[\[Mu], \[Nu]] - GAE[\[Nu], \[Mu]] GAE
\hat{\gamma }^{\mu }.\hat{\gamma }^{\nu }-\hat{\gamma }^{\nu }.\hat{\gamma }^{\mu }
StandardForm[FCI[GAE[\[Mu]]]]
(*DiracGamma[LorentzIndex[\[Mu], -4 + D], -4 + D]*)
[\[Mu], \[Nu], \[Rho], \[Sigma]] GAE
\hat{\gamma }^{\mu }.\hat{\gamma }^{\nu }.\hat{\gamma }^{\rho }.\hat{\gamma }^{\sigma }
StandardForm[GAE[\[Mu], \[Nu], \[Rho], \[Sigma]]]
(*GAE[\[Mu]] . GAE[\[Nu]] . GAE[\[Rho]] . GAE[\[Sigma]]*)
[\[Alpha]] FVD[p, \[Alpha]] // Contract GAE
\hat{\gamma }\cdot \hat{p}
[\[Alpha]] FV[p, \[Alpha]] // Contract GAE
0
In order to use Dirac algebra with D-4-dimensional objects you need to activate the t’Hooft-Veltman-Breitenlohner-Maison scheme first
["NDR"]
FCSetDiracGammaScheme
[GAE[\[Mu]] . GAD[\[Mu]]] DiracSimplify
\text{NDR}
\text{\$Aborted}
["BMHV"]
FCSetDiracGammaScheme
[GAE[\[Mu]] . GAD[\[Mu]]] DiracSimplify
\text{BMHV}
D-4
["NDR"] FCSetDiracGammaScheme
\text{NDR}