FeynCalc manual (development version)

TR

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.

See also

Overview, DiracSimplify, DiracTrace, SUNSimplify.

Examples

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 }