I need to calculate this expression:
Tr(γμγνγργσγαγβγ5)
I know that I can express this as:
Tr(γμγνγργσγαγβγ5)=−4i(gμνϵρσαβ−gμρϵνσαβ+gμσϵνραβ−gμαϵνρσβ+gμβϵνρσα+gνρϵμσαβ−gνσϵμραβ+gναϵμρσβ−gνβϵμρσα+gρσϵμναβ−gραϵμνσβ+gρβϵμνσα+gσαϵμνρβ−gσβϵμνρα+gαβϵμνρσ)
So, some of this terms are the same and some vanish. My question is how to show that.
I know that:
Tr(γμγνγργσγαγβγ5)=−4i(gμνϵρσαβ−gμρϵνσαβ+gρνϵμσαβ−gαβϵσμνρ+gσβϵαμνρ−gσαϵβμνρ)
So only six terms survive, but how?