FeynCalc manual (development version)

SUNTrace

SUNTrace[exp] is the head of color traces. By default the trace is not evaluated. The evaluation occurs only when the option SUNTraceEvaluate is set to True. It is recommended to use SUNSimplify, which will automatically evaluate all color traces involving 2 or 3 matrices in the input expression.

See also

Overview, SUNSimplify, SUNT, SUNTF, SUNF, SUND, SUNTraceEvaluate.

Examples

SUNTrace[SUNT[a, b]]

tr(Ta.Tb)\text{tr}\left(T^a.T^b\right)

SUNTrace[SUNT[a, b], SUNTraceEvaluate -> True]

δab2\frac{\delta ^{ab}}{2}

SUNTrace[SUNT[a, b]] // SUNSimplify

δab2\frac{\delta ^{ab}}{2}

SUNTrace[SUNT[a, b, c]] // SUNSimplify

dabc4+14ifabc\frac{d^{abc}}{4}+\frac{1}{4} i f^{abc}

SUNTrace[SUNT[a, b, c, d]] // SUNSimplify[#, SUNTraceEvaluate -> True, SUNIndexNames -> {j}] &

14δad(CA2CF)δbc14δac(CA2CF)δbd+14δab(CA2CF)δcd18ifadjdbcj+18idadjfbcj+18dadjdbcj18dbdjdacj+18dcdjdabj\frac{1}{4} \delta ^{ad} \left(C_A-2 C_F\right) \delta ^{bc}-\frac{1}{4} \delta ^{ac} \left(C_A-2 C_F\right) \delta ^{bd}+\frac{1}{4} \delta ^{ab} \left(C_A-2 C_F\right) \delta ^{cd}-\frac{1}{8} i f^{adj} d^{bcj}+\frac{1}{8} i d^{adj} f^{bcj}+\frac{1}{8} d^{adj} d^{bcj}-\frac{1}{8} d^{bdj} d^{acj}+\frac{1}{8} d^{cdj} d^{abj}

SUNTrace[SUNT[a, b, c, a, b, c]] // SUNSimplify

14(CA2+1)CF(CA2CF)\frac{1}{4} \left(C_A^2+1\right) C_F \left(C_A-2 C_F\right)