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nrqed

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I have done multiloop QFT calculations but when I get back to the fundamentals, something is really bugging me.

There are several issues but let m start with a question that would seem very simple:

Consider a scalar quntum field operator Phi(x). What is the meaning of the quantity [itex] c\equiv <0|\Phi(y)\Phi(x)|0>[/itex]?

where x and y are spacetime points.

Simple enough, no? It seems to me that this should be the amplitude corresponding to the creation of a particle at x and its annihilation at y. So the square of this (|c|^2) should be the probability that, given that a particle was created at x, it is annihilated at y.

Peskin and Schroeder even describe this as the "amplitude for a particle to propagate from x to y" (page 27..their x and y are switched though).

So we could imagine a reaction taking place at x, a particled described by x being created there, propagating to spacetime point y where there is a detector and being detected there.

And yet, this quantity does not vanish for spacelike intervals!

Then P&S sat, very mysteriously

**"to really discuss causality, we ask not whether particles can propagate over spacelike intervals, but whether a measurement performed at one point can affect a measurement at another point whose separation from the first is spacelike"**

I wonder why this is not bothering everyone!!

If a particle can propagate faster than light, how would that not violate causality??

(This is only one bothersome aspect of the above statement. There is also the vague use of "a measurement at one point "affecting" a measurement at another point". This *begs* for a discussion on EPR type of situation and why would the world "affecting" not apply here. But I don't want to get sidetrack on this in this thread, I want to focus on the QFT aspect)

Another question concerns the "measurement" aspect. It is never clearly defined in the context of QFT,as far as I know (not in the way it is clearly defined in QM) but this is an issue that can wait for now. I would like first to understand the "faster than light propagation" issue and why it is deemed ok!