You are confusing nonlinearities in the field equations of quantum field theory with nonlinearities in the time evolution of states. They are completely different. The former exist in standard QFT, the latter do not.
Yes. But the starting point is counting branches in simpler situations. See also Carroll & Sebens, who elaborate basically the same idea, with slightly different language:
https://arxiv.org/abs/1405.7907
When you plug in the right-hand side of the 2nd equation in (6.8) for ##\phi(x)##, you need to use two different dummy integration 4-momenta for each of the two factors of ##\phi(x)## in each term; call these ##p## and ##p'##. Then when doing the ##d^4x## integral, you will get...
Because you still need rules to decide when to modify the state by chopping off branches. If you do it under the wrong circumstances, you will destroy observable quantum coherence effects.
Psi-epistemic interpretations have all sorts of other problems as well:
https://arxiv.org/abs/1303.2834
Lüders rule, as I understand it (see below), seems to require an observer outside the system being measured. This is not the case in QFT, where observers and everything else are comprised of excitations of the quantum fields.
http://philsci-archive.pitt.edu/4111/1/Lueders_rule_BuschLahti.pdf
I don't see why it matters whether one views the quantum state as epistemic or ontological. QFT predicts a two-branched state for the post-measurement Stern-Gerlach lab (and the people in it). At what point in time, and according to what mathematical rule, do we throw away one branch?
Yes, I think so. Just by dimensional analysis, ##\langle 0|\phi(x)\phi(x+\epsilon)|0\rangle\sim 1/\epsilon^2##, so the integral should be finite (all this is in 4 spacetime dimensions).
It means the uncertainty in the value of the field at a point is infinite. Since it's not possible to measure the value of a field at an exact mathematical point, this is not a significant issue.
If you multiply together fields at slightly different points, you can express the result as a sum...
What is the mathematical description of the collapse process?
Let's say we're going to do a Stern-Gerlach experiment. We isolate the lab completely from any external environment. We put the lab (and everything in it, including the experimenters) in an initial pure state, with the experiment...
A quantum description of photons requires quantizing the electromagnetic field. This is discussed in any textbook on quantum field theory or quantum optics, and in many quantum-mechanics textbooks. This will result in operators that create and destroy photons with definite momentum and...
You need to have a consistent set of conventions for the amplitude and the factors that ##|M_{if}|^2## is multiplied by. Different texts use different conventions.