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Dec 28, 2012 at 15:06 comment added Igor Khavkine @Muon, the interpretation of such correlations in terms of particle states is often thrown about in informal discussions, but is somewhat subtle to make precise. I think it is simpler to think of such correlations as a generalization of statistical moments of random variables $J(z)$ and $\phi(z)$ with respect to a probability distribution defined by the state $|0\rangle$. If you want to get your hands on a very simppe model with almost all the same features, I recommend studying the quantum sinmple harmonic oscillator.
Dec 28, 2012 at 2:54 comment added user2013 Thank you for the answer, Igor. I am now happy to know that holomorphicity may be interpreted as a field equation. May I ask what the fields $\phi(z)$ and $J(z)$ stands for in this context? Is $\langle0| J(z)J(w)|0\rangle$ the amplitude to observe a particle at $z$ after a particle is created at $w$ or something?
Dec 28, 2012 at 0:25 history answered Igor Khavkine CC BY-SA 3.0