The first three terms are the scalar kinetic, mass, and $n$-point interaction terms. The remaining terms are the field-strength, mass, and coupling <counterterm>[counterterms]. The momentum-space rules are
$$
\frac{i}{p^2-m^2+i\epsilon},\qquad -i\lambda,
\qquad i(\delta_Zp^2-\delta_{m^2}),\qquad -i\delta_\lambda,
$$
for 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.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-304/3/a/solution