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

Table of contents
- Solution 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.

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