FCTraceExpand[exp] expands traces of Dirac and SU(N) matrices using linearity of the trace.
The traces themselves are not evaluated.
Overview, DiracTrace, SUNTrace.
ex = DiracTrace[GA[\[Mu]] . (GS[p1] + m1) . GA[\[Nu]] . (GS[p2] + m2) . GA[\[Rho]] +x]\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}+\text{m1}\right).\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}+\text{m2}\right).\bar{\gamma }^{\rho }+x\right)
FCTraceExpand[ex]\text{m1} \;\text{m2} \;\text{tr}\left(\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\bar{\gamma }^{\rho }\right)+\text{m1} \;\text{tr}\left(\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}\right).\bar{\gamma }^{\rho }\right)+\text{m2} \;\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}\right).\bar{\gamma }^{\nu }.\bar{\gamma }^{\rho }\right)+\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}\right).\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}\right).\bar{\gamma }^{\rho }\right)+\text{tr}(1) x
FCTraceExpand[ex, DotSimplify -> False]\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}+\text{m1}\right).\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}+\text{m2}\right).\bar{\gamma }^{\rho }\right)+\text{tr}(1) x
FCTraceExpand[ex, DiracTrace -> False]\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}+\text{m1}\right).\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}+\text{m2}\right).\bar{\gamma }^{\rho }+x\right)
a*DiracTrace[GA[\[Mu]] . (GS[p1] + m1) . GA[\[Nu]]] + b*DiracTrace[GA[\[Mu]] . (GS[p2] + m2) . GA[\[Nu]]]
FCTraceExpand[%, Momentum -> {p1}]a \;\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}+\text{m1}\right).\bar{\gamma }^{\nu }\right)+b \;\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}+\text{m2}\right).\bar{\gamma }^{\nu }\right)
a \left(\text{m1} \;\text{tr}\left(\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }\right)+\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p1}}\right).\bar{\gamma }^{\nu }\right)\right)+b \;\text{tr}\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{\text{p2}}+\text{m2}\right).\bar{\gamma }^{\nu }\right)
At the moment SUNTrace automatically expands its
content, so here FCTraceExpand is not needed. However, this
may change in future.
ex = SUNTrace[SUNT[i, j, k] + SUNT[l, m, n]]\text{tr}(T^i.T^j.T^k)+\text{tr}(T^l.T^m.T^n)
FCTraceExpand[ex]\text{tr}(T^i.T^j.T^k)+\text{tr}(T^l.T^m.T^n)
FCTraceExpand[ex, SUNTrace -> False]\text{tr}(T^i.T^j.T^k)+\text{tr}(T^l.T^m.T^n)