DiracGamma
DiracGamma[x, dim]
is the head of all Dirac matrices and slashes (in the internal representation). Use GA
, GAD
, GS
or GSD
for manual (short) input.
DiracGamma[x, 4]
simplifies to DiracGamma[x]
.
DiracGamma[5]
is γ5.
DiracGamma[6]
is (1+γ5)/2.
DiracGamma[7]
is (1−γ5)/2.
See also
Overview, DiracGammaExpand, GA, DiracSimplify, GS, DiracTrick.
Examples
γˉ5
DiracGamma[LorentzIndex[\[Alpha]]]
γˉα
A Dirac-slash, i.e., γμqμ, is displayed as γ⋅q.
γˉ⋅q
DiracGamma[Momentum[q]] . DiracGamma[Momentum[p - q]]
(γˉ⋅q).(γˉ⋅(p−q))
DiracGamma[Momentum[q, D], D]
γ⋅q
GS[p - q] . GS[p]
DiracGammaExpand[%]
(γˉ⋅(p−q)).(γˉ⋅p)
(γˉ⋅p−γˉ⋅q).(γˉ⋅p)
ex = GAD[\[Mu]] . GSD[p - q] . GSD[q] . GAD[\[Mu]]
γμ.(γ⋅(p−q)).(γ⋅q).γμ
4((p−q)⋅q)+(D−4)(γ⋅(p−q)).(γ⋅q)
D(γ⋅p).(γ⋅q)−Dq2−4(γ⋅p).(γ⋅q)+4(p⋅q)
DiracGamma
may also carry Cartesian indices or appear contracted with Cartesian momenta.
DiracGamma[CartesianIndex[i]]
γi
DiracGamma[CartesianIndex[i, D - 1], D]
γi
DiracGamma[CartesianMomentum[p]]
γ⋅p
DiracGamma[CartesianMomentum[p, D - 1], D]
γ⋅p
Temporal indices are represented using ExplicitLorentzIndex[0]
DiracGamma[ExplicitLorentzIndex[0]]
γˉ0