TR[exp] calculates the Dirac trace of
exp.
If the option SUNSimplify is set to True
(default), SU(N) algebra is simplified
as well.
Notice that TR is a legacy function that should not be
used in new codes. Instead, you can wrap your string Dirac matrices with
DiracTrace and subsequently apply
DiracSimplify to calculate the trace.
Overview, DiracSimplify, DiracTrace, SUNSimplify.
GA[\[Mu], \[Nu]]
TR[%]\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }
4 \bar{g}^{\mu \nu }
TR[(GSD[p] + m) . GAD[\[Mu]] . (GSD[q] - m) . GAD[\[Nu]]]-4 \left(m^2 g^{\mu \nu }+g^{\mu \nu } (p\cdot q)-p^{\nu } q^{\mu }-p^{\mu } q^{\nu }\right)
TR[GA[\[Mu], \[Nu], \[Rho], \[Sigma], 5]]-4 i \bar{\epsilon }^{\mu \nu \rho \sigma }
TR[GS[p, q, r, s]]4 \left(\left(\overline{p}\cdot \overline{s}\right) \left(\overline{q}\cdot \overline{r}\right)-\left(\overline{p}\cdot \overline{r}\right) \left(\overline{q}\cdot \overline{s}\right)+\left(\overline{p}\cdot \overline{q}\right) \left(\overline{r}\cdot \overline{s}\right)\right)
TR[(GS[p] + m) . GA[\[Mu]] . (GS[q] + m) . GA[\[Mu]], Factoring -> True]8 \left(2 m^2-\overline{p}\cdot \overline{q}\right)
TR[GA[\[Alpha], \[Beta]], FCE -> True]4 \bar{g}^{\alpha \beta }
```mathematica GA[[Mu], [Nu]] SUNT[b] . SUNT[c] SUNDelta[c, b]
TR[%]
```mathematica
\delta ^{bc} T^b.T^c \bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }
4 C_F \bar{g}^{\mu \nu }