FeynCalc manual (development version)

DiracSigmaExplicit

DiracSigmaExplicit[exp] inserts in exp for all DiracSigma its definition. DiracSigmaExplict is also an option of DiracSimplify. DiracSigmaExplict is also an option of various FeynCalc functions that handle the Dirac algebra.

See also

Overview, DiracGamma, DiracSigma.

Examples

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)

GSD[p] . DiracSigma[GAD[\[Mu]], GAD[\[Nu]]] . GSD[q] 
 
DiracSigmaExplicit[%]

(\gamma \cdot p).\sigma ^{\mu \nu }.(\gamma \cdot q)

\frac{1}{2} i \left((\gamma \cdot p).\gamma ^{\mu }.\gamma ^{\nu }.(\gamma \cdot q)-(\gamma \cdot p).\gamma ^{\nu }.\gamma ^{\mu }.(\gamma \cdot q)\right)