DiracSigma[a, b] stands for I/2(a.b-b.a) in 4 dimensions.
a and b must have head
DiracGamma, GA or GS. Only
antisymmetry is implemented.
DiracSigma[GA[\[Alpha]], GA[\[Beta]]]
DiracSigmaExplicit[%]\sigma ^{\alpha \beta }
\frac{1}{2} i \left(\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }-\bar{\gamma }^{\beta }.\bar{\gamma }^{\alpha }\right)
DiracSigma[GA[\[Beta]], GA[\[Alpha]]]-\sigma ^{\alpha \beta }
DiracSigma[GS[p], GS[q]]
DiracSigmaExplicit[%]\sigma ^{pq}
\frac{1}{2} i \left(\left(\bar{\gamma }\cdot \overline{p}\right).\left(\bar{\gamma }\cdot \overline{q}\right)-\left(\bar{\gamma }\cdot \overline{q}\right).\left(\bar{\gamma }\cdot \overline{p}\right)\right)
The antisymmetry property is built-in
DiracSigma[GA[\[Alpha]], GA[\[Alpha]]]0