Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-304/2/a/solution

The first three terms are the renormalized kinetic, mass, and quartic interaction terms. The remaining three are counterterms: gives wave-function renormalization, renormalizes the mass, and renormalizes the four-point coupling. With all momenta entering a vertex, the momentum-space Feynman rules are
together with momentum conservation at every vertex and an integral for each independent loop momentum.

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