The photoelectric effect alone indeed isn't a definitive proof of quantization of EM field, but together with Bothe&Geiger's experiment in 1925 it did prove semiclassical treatment is not good. PF user Ben Crowell had a post in PF, I couldn't find it, but here's his stackexchange post...
I think the same, but this is still a bit speculative. After all, it's a infinite sum of almost arbitrarily complicated diagrams, and it won't be surprising if nasty stuff happens.
Weinberg uses this to argue photon mass is protected during renormalization, i.e. radiative corrections don't give...
I'm reading the QFT textbook by Weinberg. In volume one chapter 10 page 451, at the lower part of the page he says,
\Pi^*_{\mu\nu}(q) is the sum of all one-photon-irreducible graphs, with the two external photon propagators omitted, and q being the external photon momentum.
Weinberg states it...
I think OP might have confused the 3-dimensional rep of SO(3) that describes spin-1 in QM and 3-dimensional real vector rep of SO(3). If I remember correctly, the only difference is that the former is defined on complex vector space and the latter is on real vector space, besides this, these two...
Even if the phase is eiθ, then interchanging two indistinguishable particles will give us a_n^2=e^{i\theta}a_n^2, which again implies a_n^2=0 as long as e^{i\theta}\neq1, and then by the argument in my original post, the phase has to be -1. Besides, I can't see another way to incorporate Pauli...
Why not, say if m means spin up and n means spin down, the sum is just another creation operator which creates a state of superposition of spin up and down.
Then for fermions I doubt if this argument is still applicable since we have Pauli exclusion, which does not allow the existence of such...
In Weinberg's textbook on QFT(google book preview), he discussed the phase acquired after interchanging particle labels in the last paragraph of page 171 and the footnote of page 172. It seems he's suggesting interchanging particles of same species but different spin states will only bring a...
In a multi-particle Hilbert space, any operator can be expressed as a polynomial of creation and annhilation(c/a) operators, so if we agree we need a multi-particle physics in the first place, there's nothing wrong to use c/a operators to express everything. As for why we prefer to use it than...
But then it is hard to see how to apply residue calculus since the denominator is in terms of energy. If we want we can convert the momentum integral into energy integral, since d^3\mathbf{p}=p^2\sin\theta dpd\theta d\phi, and E_\alpha=\sqrt{p^2+m^2}, since by definition E_\alpha is the energy...
I was reviewing the first few chapters of Weinberg VolI and found a hole in my understanding in page 112, where he tried to show in the asymptotic past t=-\infty, the in states coincide with a free state. In particular, he argued the integral \int...
I guess my confusion comes from the following content of quite a few textbooks:
(1)Relativistic wave equations are understood as field equations(EM,Dirac etc.)
(2)c-number solutions of field equations are understood as classical fields(this is usually mentioned for EM field, but I presume this...
But taking Sakurai's view has its own confusing issues: for Dirac field the ket and classical field(or Dirac wavefunction) is related by \psi(x)=\langle 0|\hat{\psi}(x)|p\rangle not expectation values(c.f.sakurai chap 3-10; weinberg chap 14.1), and it seems strange to me to give different...