I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum. Consider a real (or complex, with + in the right places) scalar particle (a Klein-Gordon field). Now consider the propagator (or correlation function) G(x-y)= <0|phi(y) phi(x) |0> (where I assume that the two operators are correctly time-ordered already) My questions are related to how exactly to interpret this. A standard interpretation seems to be to say that since phi(x) is (or contains) a creation operator for a virtual particle, this describes the creation of a virtual particle at x and its destruction at y. My first problem is that intuitively this does not make much sense, because the vacuum is completely Lorentz invariant, so for each particle created at x (and later destroyed at y), there would be another virtual particle that was created at an earlier time and is destroyed at x. After all, the vacuum is absolutely stationary. So here is my Question 1: In what sense is this interpretation to be understood? I could try to understand it in a sense from a path integral interpretation. I look at the vacuum-to-vacuum amplitude <0|0>. There I have to integrate over all field configurations that have different contributions according to their action. For each configuration, I could calculate phi(y)phi(x), and summing over all configurations with the appropriate weights, I could see the correlation. This would give meaning to the term "vacuum fluctuation" if applied to each configuration separately - if the field value is very large at x and if y is a near-by point, the field will with higher probability be large there as well because otherwise the action would be very large. I think this is how correlation functions are used in lattice gauge theory. So Question 2 is simply: Is this interpretation within the path integral formalism correct? If so, is there a way to transfer it to the canonical formalism? Furthermore, on the other hand, standard lore is that for any operator Q <0|Q|0> is the vacuum expectation value of Q, i.e., it is the value I would get if I were to perform a very large number of measurements of the variable Q. So if I now set Q=phi(y)phi(x), this would tell me that G(x-y) is the expectation value I would get if I measure first phi(x), then phi(y) and then calculate the product of both. So let's create infinitely many copies of the vacuum (so I can perform enough measurements to get an expectation value). In each of my copies, I now perform a measurement of the field at x. This will create a new state of my universe. In quantum mechanics, I would say that this new state would be an eigenstate to phi(x) (which would then evolve), but - here is my Question 3 - does phi(x) actually *have* eigenstates? (If so, what are they, especially if phi is a complex field?) And is there actually any way I could perform this measurement of phi? How do you measure a field value of a quantum field anyway? (Again, especially in the case of a complex field?) Since I'm now in a new state phi(x)|0>, I could interpret <0|phi(y) phi(x) |0> as the matrix element of getting from my new state back to the vacuum state by applying another field measurement phi(y). This would then mean that <0|phi(y) phi(x) |0> is something like the probability of getting from vacuum back to a vacuum if I apply two subsequent measurements of phi (similar to Fermi's golden rule, where a matrix element also gives a transition probability). So finally, my question 4: Would this be a correct interpretation of <0|phi(y) phi(x) |0>? This is my first post here - I've read a lot hereabouts, but did not really find an answer to these question. Thanks for any help.