With all momenta incoming, the <Feynman rules> are
$$
\text{propagator: }\frac{i}{p^2-m^2+i\epsilon},
$$
$$
\text{three-point vertex: }
2i\lambda\sum_{j=1}^3(p_j^2-m^2),
$$
and
$$
\text{four-point vertex: }
4i\lambda^2\left(\sum_{j=1}^4p_j^2-3m^2\right).
$$
Each vertex includes its momentum-conserving delta function. The combinatorial factors follow by assigning the identical fields to the differentiated and undifferentiated slots in every possible way.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 4 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-301/4/b/solution