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)