Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 304 / 2 / a

The first three terms are the renormalized kinetic, mass, and quartic interaction terms. The remaining three are counterterms: $\delta Z$ gives wave-function renormalization, $\delta m^2$ renormalizes the mass, and $\delta \lambda$ renormalizes the four-point coupling. With all momenta entering a vertex, the momentum-space Feynman rules aretogether with momentum conservation at every vertex and an integral $\int d^{d}p/(2\pi {)}^d$ for each independent loop momentum.