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.