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 \gamma ^5.
DiracGamma[6] is (1+\gamma ^5)/2.
DiracGamma[7] is (1-\gamma ^5)/2.
Overview, DiracGammaExpand, GA, DiracSimplify, GS, DiracTrick.
DiracGamma[5]\bar{\gamma }^5
DiracGamma[LorentzIndex[\[Alpha]]]\bar{\gamma }^{\alpha }
A Dirac-slash, i.e., \gamma ^{\mu }q_{\mu}, is displayed as \gamma \cdot q.
DiracGamma[Momentum[q]] \bar{\gamma }\cdot \overline{q}
DiracGamma[Momentum[q]] . DiracGamma[Momentum[p - q]]\left(\bar{\gamma }\cdot \overline{q}\right).\left(\bar{\gamma }\cdot \left(\overline{p}-\overline{q}\right)\right)
DiracGamma[Momentum[q, D], D] \gamma \cdot q
GS[p - q] . GS[p]
DiracGammaExpand[%]\left(\bar{\gamma }\cdot \left(\overline{p}-\overline{q}\right)\right).\left(\bar{\gamma }\cdot \overline{p}\right)
\left(\bar{\gamma }\cdot \overline{p}-\bar{\gamma }\cdot \overline{q}\right).\left(\bar{\gamma }\cdot \overline{p}\right)
ex = GAD[\[Mu]] . GSD[p - q] . GSD[q] . GAD[\[Mu]]\gamma ^{\mu }.(\gamma \cdot (p-q)).(\gamma \cdot q).\gamma ^{\mu }
DiracTrick[ex]4 ((p-q)\cdot q)+(D-4) (\gamma \cdot (p-q)).(\gamma \cdot q)
DiracSimplify[ex]D (\gamma \cdot p).(\gamma \cdot q)-D q^2-4 (\gamma \cdot p).(\gamma \cdot q)+4 (p\cdot q)
DiracGamma may also carry Cartesian indices or appear contracted with Cartesian momenta.
DiracGamma[CartesianIndex[i]]\overline{\gamma }^i
DiracGamma[CartesianIndex[i, D - 1], D]\gamma ^i
DiracGamma[CartesianMomentum[p]]\overline{\gamma }\cdot \overline{p}
DiracGamma[CartesianMomentum[p, D - 1], D]\gamma \cdot p
Temporal indices are represented using ExplicitLorentzIndex[0]
DiracGamma[ExplicitLorentzIndex[0]]\bar{\gamma }^0