By Stetz A.W.

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Here as always, these constants cancel between the numerator and denominator. Often in doing perturbation theory, we are concerned with the correlation function for two free particles. In this case we replace |Ω with |0 . The denominator is then proportional to 0|0 = 1, so we can ignore it altogether. Back at the end of Chapter 2, I introduced the notion of a generating function. 65), which I repeat here for reference. 38) We take advantage of recent developments by upgrading these formulas in two ways: (1) replacing the Qi ’s with the fields, ϕ(x), and (2) taking the limit T → ∞(1 − i ).

The momenta of the final state particles are determined by our apparatus. The rules for Feynman diagrams discussed briefly above also have a simpler form in momentum space. Define the momentum space Green’s functions in the obvious way. 75) I call your attention to the ± signs in the exponential. To some extent the sign doesn’t matter, since G(x) = G(−x) and ∆(p) = ∆(−p). 5. MOMENTUM SPACE 53 when x or p appear as integration variables, one is always free to replace x → −x or p → −p. In one respect, however, the signs are all-important.

Lim T →∞(1−i ) (e−iE0 T Ω|ϕa )−1 e−iHT |ϕa . 35) Insert (35) into (34). 36) I remarked previously that the measure D[ϕ] produced weird normalization constants. Here as always, these constants cancel between the numerator and denominator. Often in doing perturbation theory, we are concerned with the correlation function for two free particles. In this case we replace |Ω with |0 . The denominator is then proportional to 0|0 = 1, so we can ignore it altogether. Back at the end of Chapter 2, I introduced the notion of a generating function.

### Advanced quantum mechanics by Stetz A.W.

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