By Stetz A.W.
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Terms like this in the Wick sum. 74) Forgive me if I gloat a bit. A few paragraphs ago we had some algebra, which, if done correctly, would have yielded 105 terms. Now we draw a few pictures, and the answer is obvious by inspection. These pictures are called Feynman diagrams. =81 terms, These are all pathological in the sense that the ω point is connected to itself by at least one line. It is a general rule that all Feynman diagrams with loops give rise to divergent integrals. This is ultimately related to the fact that there are parameters such as the mass and coupling constant (or charge) of a particle that are fundamentally mysterious.
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. 65), which I repeat here for reference.
First expand Z[J]/Z in an exponential series. 56) The second term is easy to understand. 57) Suppose our source consists of two local centers of activity, so that J(x) = J0 [δ(x − x1 ) + δ(x − x2 )]. 58) The D(0) is meaningless. It’s an artifact of our delta function sources. The other term is simply the probability of a particle to be created by the source at x1 (when the source was turned on) and reabsorbed at x2 (when the source was turned off) and vice versa. Now calculate the two-point function corresponding to iW without specifying the nature of the sources.
Advanced quantum mechanics by Stetz A.W.