Trick[exp] performs several basic simplifications without expansion. Trick[exp] uses Contract, DotSimplify and SUNDeltaContract.
Overview, Calc, Contract, DiracTrick, DotSimplify, DiracTrick.
This calculates g^{\mu \nu} \gamma _{\mu } and g_{\nu }^{\nu} in D dimensions.
Trick[{GA[\[Mu]] MT[\[Mu], \[Nu]], MTD[\[Nu], \[Nu]]}]\left\{\bar{\gamma }^{\nu },D\right\}
FV[p + r, \[Mu]] MT[\[Mu], \[Nu]] FV[q - p, \[Nu]]
Trick[%]\bar{g}^{\mu \nu } \left(\overline{q}-\overline{p}\right)^{\nu } \left(\overline{p}+\overline{r}\right)^{\mu }
\overline{p}\cdot \overline{q}-\overline{p}\cdot \overline{r}-\overline{p}^2+\overline{q}\cdot \overline{r}
Trick[c . b . a . GA[d] . GA[e]]a b c \bar{\gamma }^d.\bar{\gamma }^e
Trick[c . b . a . GA[d] . GA[e]] // FCE // StandardForm
(*a b c GA[d] . GA[e]*)