DiracGamma

Description

DiracGamma[x, dim] is the head of all Dirac matrices and slashes (in the internal representation). Use DiracMatrix (or GA, GAD) and DiracSlash (or GS, GSD) for manual (short) input. DiracGamma[x, 4] simplifies to DiracGamma[x]. DiracGamma[5] is (γ^5). DiracGamma[6] is (1 + (γ^5))/2.  DiracGamma[7] is (1 - (γ^5))/2.

See also:  DiracGammaExpand, DiracMatrix, DiracSimplify, DiracSlash, DiracTrick.

Examples

DiracGamma[5]

DiracGamma[LorentzIndex[α]]

A Dirac-slash, i.e., (γ^μ) (Subscript[q, μ]), is displayed as γ·q.

DiracGamma[Momentum[q]]

DiracGamma[Momentum[q]]  .  DiracGamma[Momentum[p - q]]

DiracGamma[Momentum[q, D], D]

a1 = GS[p - q] . GS[p]

a2 = DiracGammaExpand[a1]

a3 = GAD[μ] . GSD[p - q] . GSD[q] . GAD[μ]

a4 = DiracTrick[a3]

a5 = DiracSimplify[a4]

Clear[a1, a2, a3, a4, a5]