I apologize for the vague title, I don't know the names for the objects I'm asking about, which also made it hard to search for more information on them.(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading Zee's QFT in a Nutshell and have the feeling I'm missing something. When introducing the path integral formalism, he defines a quantity

[tex]

Z(J) = \langle 0 | e^{-i H T} | 0 \rangle

[/tex]

which, if I'm reading it right, should represent the amplitude of "propagating from vacuum to vacuum". He works out what [itex]Z(J)[/itex] looks like and eventually defines

[tex]

Z(J) = e^{i W(J)}.

[/tex]

The exponential turns out to be

[tex]

W(J) = -\frac{1}{2} \int \int d^4 x d^4 y J(x) D(x-y) J(y).

[/tex]

At first I sort of skipped over all of this, but a good understanding turns out to be important later on. My problem is that I don't fully understand what these quantities represent. What does this vacuum-to-vacuum propagation mean? What does that leave [itex]W(J)[/itex] to mean? Apparently [itex]W(J)[/itex] represents some kind of amplitude for a particle propagating from a disturbance at [itex]x[/itex] to a disturbance at [itex]y[/itex], and though that doesn't soundwrong, I don't understand why it is right either. Zee bases a lot of things on a sentence starting with "We see that [itex]W(J)[/itex] is only large when...", but why does it need to be large?

If anyone could get me on track with these things (and maybe provide some names), I would appreciate it. I'm just looking for the right way to interpret them.

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# Z(J) and W(J)

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