Weinberg, Vol. 1: Path Integrals Query

[Reggaerules]

I am trying to study QFT from Weinberg's Vol. 1.

I am at the moment stuck at the path integral quantization of QED (Weinberg's treatment).

I am not sure how he integrates out the matter field momenta (for the spinor field) in eq. (9.6.5). I thought for spinor fields you don't do that.

I thought that there should be integration with respect to p_m as given in eq. (9.5.56).

Any help will be much appreciated.

 

[Avodyne]

I think he just didn't bother to write $d\psi^\dagger$. This is essentially a matter of convention as to whether we think of $\psi^\dagger$ as an independent field or not.

 

[Reggaerules]

QFT: Path Integrals, Weinberg Vol. 1

I had e-mailed SW about this, he told me that it was integrated out.

My understanding is fairly minimal, but from (9.5.1), (9.5.49) and (9.5.52), I didn't think
the adjoint spinor could be integrated out. If you could give me a reference, and/or a hint that would be great. I thought one needed equal amounts of \psi and \psi adjoint terms.

Thanks for your message.