It turns out that it was an error on my part. For example, for rotation by angle \phi around the 3 axis, I get
e^{-i \phi J_3} since \omega_{12} = - \phi.
In equation (2.5.47),
I am getting
U(R(\hat p) = e^{+i \phi J_3} e^{+i \theta J_2}
Instead of the "-" signs in the exponential. This makes a phase difference under parity and time reversal of a massless particle.
Is this one of the active rotation vs. passive rotation problem? If so...
Last line of page 17, volume 2. Also the measure in 15.4.16 does not have any adjoint spinor terms. I am just afraid to move on (since I am studying QFT by myself). Not sure why Weinberg does this consistently. If I understand it for the simple case of QED (I haven't yet started Vol. 2), I am...
Wow, you are much more proficient in this than I am. But, I think my questions remains...mind you, I don't have any problems with his conclusions.
As you pointed out, you integrated the positions and momentums of the fermion fields at same time. Weinberg just integrates out the momenta...
I have gone through the entire chapter, but nothing seems to help me. In the development of the spinor path integral, Weinberg requires d \psi^dagger (d p_m as he calls in the general formulation) in the integral measure, but, when he does QED, this does not appear in the integral measure. If I...
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...
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...