Posted: Sep 14, 2011 7:28 am
zaybu wrote:twistor59 wrote:
I'm quite aware that spacetime position in QFT is not an operator, but rather a parameter. What I'm talking about is a position operator, not x, which can be defined for electrons (for example), but not for photons.
You've lost me there, twistor. Which position operator is there in QFT?
Position operators like this one. They don't generalize to photons.
Another way to put it is that, for an electron, I can define a wavefunction Ψ such that |Ψ|2d3x represents the probability of finding the particle within the volume d3x. (I'm ignoring spin) You can in principle localise the electron to a volume as small as you like, within the constraints imposed by the uncertainty principle.
If you try to define such a wavefunction for the photon, you enter an area of ongoing heated debate. If you set up the candidate wavefunction, and then try to establish the pdf of the photon position, you realize that you can only do this by looking at what happens to test charges (since these are what establish the photon's presence or absence). But this interaction with test charges at any point x is determined by the value of the EM fields E(x), B(x). However it turns out that E(x), B(x) depend non locally on the candidate wavefunction, so the project fails.
So, for me, photons are less "particle like" than electrons, and I think it would be clearer if we encouraged people to refer to "field quanta", since quantum fields are the primitive entities, not particles. "Particles" belong more to first quantization treatments, and photons seem very reluctant to be treated in this way !