Hello~
Recently I became to use FeynCalc.
It looks great ! I am studying to use this package. But nowaday
it seems that I can not understand well the usage of multiplication
operator, for example, the usage of '.' .
In HTLM document in this webpage, dot '.' means non-commutive
operator product. LC symbol is commutive stuff. So we can treat LC
as scalar. But when we put it into trace, it seems that there is some
problem.
Please, see my problem as following.
What is right? And why ohter are wrong (Why they are different) ?
1
FV[p, \mu]*LC[\mu,\nu,\alpha,\beta]*
(
(GA[k_1]_ i a5).GA[\nu].(GS[k_2]+i a1).gamma.(GS[p]-GS[k_1+i a3]).GA[5]
) //
Tr //
Contract
2
FV[p, \mu]*
(
(GA[k_1]_ i a5).LC[\mu,\nu,\alpha,\beta]*GA[\nu].(GS[k_2]+i a1).gamma.(GS[p]-GS[k_1+i a3]).GA[5]
) //
Tr //
Contract
3
FV[p, \mu]*
(
(GA[k_1]_ i a5)*LC[\mu,\nu,\alpha,\beta]*GA[\nu].(GS[k_2]+i a1).gamma.(GS[p]-GS[k_1+i a3]).GA[5]
) //
Tr //
Contract
-------------
i : imaginary number
a1,a3,a5 : constant
gamma : second rank tensor which I difined. It has no problem.
thanks
regards
huiyoung
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