Is the big picture of quantum field theory that:
- There are fields (EM, electron, Higgs, gravity, etc.)
- A field can be described by a wavefunction indicating the probability density of 1 or more 'particles,' which are just localizations/quantizations of the field
- One field affecting another is an 'interaction'
- Would that mean that photons, as the force-carrier of the EM field, have their own field? I thought that photons were just localizations of the EM field.
- Why aren't electrons similarly localizations of the EM field?
I know this is a very broad question for a Stack Exchange site, but I have yet to find a treatment that covers these questions that isn't either uselessly general (i.e. 'popular') or extremely, extremely specific (i.e. textbooks). Even the few in-between treatments seem to avoid these very fundamental concepts.