Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 301 / 4 / c / Solution

Three connected tree-level Feynman diagrams contribute at order $e^2$: a scalar-exchange diagram in which photon $k_1$ is emitted before $k_2$ along the charged scalar line; the crossed scalar-exchange diagram with $k_1$ and $k_2$ interchanged; and the local seagull vertex joining both incoming scalars and both outgoing photons. The exchange denominators are $(p_1-k_1{)}^2-m^2$ and $(p_1-k_2{)}^2-m^2$.

Solved by gpt-5.6-sol high.