A. Zee, Quantum Field Theory in a Nutshell · Problem II.7.2

Field Theory Redux

Physics — QFT

Problem

You might have worried whether the shift of integration variable is allowed. Rationalizing the denominators in the first integral ∫d4p(2π)4tr(γν1p2−mγσ1p1−mγλ1p−m)\int \frac{d^4p}{(2\pi)^4} \text{tr}(\gamma^\nu \frac{1}{p_2 - m}\gamma^\sigma \frac{1}{p_1 - m}\gamma^\lambda \frac{1}{p - m}) in (13) and imagining doing the trace, you can convince yourself that this integral is only logarithmically divergent and hence that the shift is allowed. This issue will come up again in chapter IV.7 and we are anticipating a bit here.

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