Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 304 / 3 / a / Solution

The first three terms are the scalar kinetic, mass, and $n$-point interaction terms. The remaining terms are the field-strength, mass, and coupling counterterms. The momentum-space rules arefor a propagator, an $n$-leg interaction vertex, a two-leg counterterm insertion, and an $n$-leg counterterm vertex, respectively, together with momentum conservation at every vertex.