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.
Overview, SUNSimplify, SUNT, SUNTF, SUNF, SUND, SUNTraceEvaluate.
[SUNT[a, b]] SUNTrace
\text{tr}\left(T^a.T^b\right)
[SUNT[a, b], SUNTraceEvaluate -> True] SUNTrace
\frac{\delta ^{ab}}{2}
[SUNT[a, b]] // SUNSimplify SUNTrace
\frac{\delta ^{ab}}{2}
[SUNT[a, b, c]] // SUNSimplify SUNTrace
\frac{d^{abc}}{4}+\frac{1}{4} i f^{abc}
[SUNT[a, b, c, d]] // SUNSimplify[#, SUNTraceEvaluate -> True, SUNIndexNames -> {j}] & SUNTrace
\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}
[SUNT[a, b, c, a, b, c]] // SUNSimplify SUNTrace
\frac{1}{4} \left(C_A^2+1\right) C_F \left(C_A-2 C_F\right)