Hello everyone! I need to automatically calculate traces of products of (for example) three Gell-Mann matrices:
SUNTrace[SUNT[SUNIndex[a]].SUNT[SUNIndex[b]].SUNT[SUNIndex[c]]]
so I wrote a rule in FeynCalc that changes the trace to its explicit form:
rule = {SUNTrace[SUNT[SUNIndex[a_]].SUNT[SUNIndex[b_]].SUNT[SUNIndex[c_]]] :> 1/4 (SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]]+I SUNF[SUNIndex[a], SUNIndex[b], SUNIndex[c]])};
Obviously, this gives the correct answer for
SUNTrace[SUNT[SUNIndex[a]].SUNT[SUNIndex[b]].SUNT[SUNIndex[c]]] //. rule
BUT whenever I try another input, such as
SUNTrace[SUNT[SUNIndex[x]].SUNT[SUNIndex[y]].SUNT[SUNIndex[z]]] //. rule
I get a result with indices with underscores, such as
1/4 (SUND[SUNIndex[x_], SUNIndex[y_], SUNIndex[z_]]+I SUNF[SUNIndex[x_], SUNIndex[y_], SUNIndex[z_]])
I do not know why this is happening but it bugs me because this rule worked for me pretty well in past days and now it just doesn't work. Moreover, it is impossible to carry out the next calculations when the indices carry the underscores. Thanks everyone for helping me.
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