Wavefunction of quantzed field states

[david_d]

Hi,

Following electromegnetic field quantization, one ends up with the fock states as the energy eigenstates
of the quantized field. Considering a single mode field, the set of fock states are the single-mode energy eigenstates. Yes, these fock (or number) states are just the eigenstates of the corresponding Hamiltonian
that takes the form of an Harmonic oscillator's Hamiltonian.

Now, formally, a fock state, |n>, can be projected on the position eigenstates, <q|n>, and one ends up with
a wavefunction in coordinate representation, which resembles the eigenfunctions of a quantum-mechanical Harmonic oscillator (only now, in the case of EM field, nothing has mass).

My question is: What do these wavefunctions, in the coordinate representation, represent?
What is the physical interpretation of these wavefunctions, psi(q), for the quantized EM field?
The probabilitiy of WHAT they represent, with respect to coordinate-space?

David

 

[atyy]

There isn't a relativistic position operator.

http://www.physics.upenn.edu/~chb/phys253a/coleman/coleman.pdf (p14-16)

 

[bhobba]

The answer requires a detailed development of QFT.

Unfortunately many QFT books are written by smart practitioners for equally smart graduate students they hope to be their successors so they gloss over many important issues hoping their intended audience will nut it out themselves.

A book however has recently been released that can be tackled undergraduate that takes great care to carefully explain what's going on:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Atyy is correct, and the link he gave is of course correct. But try going through it to get the answer - good luck.

If you are really interested in QFT get the book I mentioned, take your time going through it and things will be much clearer.

I am doing just that right now - the Kindle version is a good price for a QFT text as well.

Thanks
Bill