DiracTrick[exp] contracts Dirac matrices with each other and performs several simplifications but no expansions.There are not many cases when a user will need to call this function directly. Use DiracSimplify to achieve maximal simplification of Dirac matrix chains. Regarding the treatment of \gamma^5 in D-dimensional expressions or the evaluation of expressions with tensors living in different dimensions, see the explanations on the help pages for DiracSimplify and DiracTrace.
Overview, Contract, DiracEquation, DiracGamma, DiracGammaExpand, DiracTrick, SirlinSimplify, SpinorChainTrick.
When applied to chains of Dirac matrices that do not require noncommutative expansions, contractions with other tensors, simplifications of spinor chains or evaluations of Dirac traces, DiracTrick will produce results similar to those of DiracSimplify.
GA[\[Mu], \[Nu], \[Mu]]
DiracTrick[%]\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\bar{\gamma }^{\mu }
-2 \bar{\gamma }^{\nu }
GS[p] . GS[p]
DiracTrick[%]\left(\bar{\gamma }\cdot \overline{p}\right).\left(\bar{\gamma }\cdot \overline{p}\right)
\overline{p}^2
GA[5, \[Mu], \[Nu]]
DiracTrick[%]\bar{\gamma }^5.\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }
\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\bar{\gamma }^5
(1/2 - GA[5]/2) . (-((a + GS[p + q])/b)) . (1/2 + GA[5]/2)
DiracTrick[%]\left(\frac{1}{2}-\frac{\bar{\gamma }^5}{2}\right).\left(-\frac{\bar{\gamma }\cdot \left(\overline{p}+\overline{q}\right)+a}{b}\right).\left(\frac{\bar{\gamma }^5}{2}+\frac{1}{2}\right)
-\frac{\left(\bar{\gamma }\cdot \left(\overline{p}+\overline{q}\right)\right).\bar{\gamma }^6}{b}
Dirac traces are not evaluated by DiracTrick
DiracTrace[GAD[\[Mu], \[Nu]]]
DiracTrick[%]\text{tr}\left(\gamma ^{\mu }.\gamma ^{\nu }\right)
\text{tr}\left(\gamma ^{\mu }.\gamma ^{\nu }\right)