Name: Vladyslav Shtabovenko Date: 02/11/15-07:07:41 PM Z
There is nothing special about gamma matrices in FeynCalc. The
thing is just that ComplexConjugate is meant to be applied on only
closed spinor chains, i.e. expressions of type ubar.(gamma matrices).v
that usually appear in a matrix element and not on single gamma
matrices.
The two examples you quoted make perfect sense if you consider that
GA[5] and GA[i] are inside a closed spinor chain. For
example
(ubar.g^5.v)* = (u^*_i g^0_ij g^5_jk v_k)* =
u_i g^(0*)_ij g^(5*)_jk v^*_k
since g^0 is hermitian, i.e.
(g^0_ij)* = g^(0 \dagger)_ji = g^0_ji
we get
(ubar.g^5.v)* = v^*_k g^(5 \dagger)_kj g^0_ji u_i =
- v^*_k g^0_kl g^5_lm g^0_mj g^0_ji u_i =
- v^*_k g^0_kl g^5_li u_i = - (vbar.g^5.u)
where I used that g^5\dagger = - g^0 g^5 g^0.
Cheers,
Vladyslav
> Hi,
> How are gamma matrices defined in Feyncalc?
> Becouse in a standard definition (the one by wikipedia for example)
we have
> ComplexConjugate[GA[5]]=GA[5] and
ComplexConjugate[GA[i]]=GA[0]GA[i]GA[0]
,i=0,1,2,3.
>
> whereas in Feyncalc
> ComplexConjugate[GA[5]]=-GA[5] and
ComplexConjugate[GA[i]]=GA[i].
>
> Thanks.