FeynCalc manual (development version)

DiracSigma

DiracSigma[a, b] stands for I/2(a.bb.a)I/2(a.b-b.a) in 4 dimensions.

a and b must have head DiracGamma, GA or GS. Only antisymmetry is implemented.

See also

Overview, DiracSigmaExplicit.

Examples

DiracSigma[GA[\[Alpha]], GA[\[Beta]]] 
 
DiracSigmaExplicit[%]

σαβ\sigma ^{\alpha \beta }

12i(γˉα.γˉβγˉβ.γˉα)\frac{1}{2} i \left(\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }-\bar{\gamma }^{\beta }.\bar{\gamma }^{\alpha }\right)

DiracSigma[GA[\[Beta]], GA[\[Alpha]]]

σαβ-\sigma ^{\alpha \beta }

DiracSigma[GS[p], GS[q]] 
 
DiracSigmaExplicit[%]

σpq\sigma ^{pq}

12i((γˉp).(γˉq)(γˉq).(γˉp))\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]]]

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