FeynCalc manual (development version)

GAE

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] ....

See also

Overview, DiracGamma, GA, GS, GAD.

Examples

GAE[\[Mu]]

\hat{\gamma }^{\mu }

GAE[\[Mu], \[Nu]] - GAE[\[Nu], \[Mu]]

\hat{\gamma }^{\mu }.\hat{\gamma }^{\nu }-\hat{\gamma }^{\nu }.\hat{\gamma }^{\mu }

StandardForm[FCI[GAE[\[Mu]]]]

(*DiracGamma[LorentzIndex[\[Mu], -4 + D], -4 + D]*)

GAE[\[Mu], \[Nu], \[Rho], \[Sigma]]

\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]]*)

GAE[\[Alpha]] FVD[p, \[Alpha]] // Contract

\hat{\gamma }\cdot \hat{p}

GAE[\[Alpha]] FV[p, \[Alpha]] // Contract

0

In order to use Dirac algebra with D-4-dimensional objects you need to activate the t’Hooft-Veltman-Breitenlohner-Maison scheme first

FCSetDiracGammaScheme["NDR"] 
 
DiracSimplify[GAE[\[Mu]] . GAD[\[Mu]]]

\text{NDR}

\text{\$Aborted}

FCSetDiracGammaScheme["BMHV"] 
 
DiracSimplify[GAE[\[Mu]] . GAD[\[Mu]]]

\text{BMHV}

D-4

FCSetDiracGammaScheme["NDR"]

\text{NDR}