Re: On the wave function of the photon



Ben Rudiak-Gould wrote:

1. Armed with wave equations for photons and electrons, one could try to construct a "fieldless QED", using a wave function on Fock space with some sort of coupling between electron and electron+photon states. Could one in principle reproduce the predictions of QED in a theory like this? My impression is that the answer is no, because I don't see how to accommodate virtual particles in Fock space. Which leads to question

1a. How is Fock space actually related to QFT, if at all? It's described in textbooks as a way to make a relativistic quantum theory that allows for the creation and annihilation of particles, but all the successful relativistic quantum theories are field theories, which don't have particles in the first place. 

This is not true. Quantum field theories are actually about particles
and their interactions. Most QFT textbooks successfully hide this fact
by placing too much emphasis on fields. You will find quite
different and
refreshing perspective on QFT in Weinberg's vol.1. He starts with
particles, Fock space, creation and annihilation operators,
and introduces fields only as a tool for constructing
interparticle interactions. "fieldless QED" is a worthy goal, and
I suggest you to read more about that in physics/0504062.


2. Can one derive similar wave equations for generic massive/massless particles of arbitrary half-integral spin? For the other particles in the standard model? 

Bialynicki-Birula'c "photon equation"

>    i hbar d_t F = c (hbar / i) (S_x d_x + S_y d_y + S_z d_z) F,
>
> with the side condition that div F = 0, and the matrices
>
>          / 0 0  0 \         /  0 0 i \         / 0 -i 0 \
>    S_x = | 0 0 -i |   S_y = |  0 0 0 |   S_z = | i  0 0 |
>          \ 0 i  0 /         \ -i 0 0 /         \ 0  0 0 /

does not make much sense to me because it implies 3 internal degrees
of freedom. However, it is known that photons have only 2 independent
polarizations. It seems more reasonable to represent photons (as well as other massive and massless particles) by Wigner's unitary irreducible representations of the Poincare group (without inversions). Actually, photons are described
by a direct sum of two irreducible representations with helicities
(= circular polarizations) -1 and +1. You'll find more in Chapter 2 of
Weinberg's book.



.

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