Student Friendly Introduction to QFT · Problem 8.15

The core concept here is pair annihilation into photons, which happens through two distinct intermediate states depending on which particle radiates first. The key insight is that both diagrams contribute equally to the total amplitude—one where the electron emits a photon before annihilating, and one where the positron does—so you must draw both and recognize they're related by swapping the role of the two external photons. Writing the amplitude means carefully applying the Feynman rules: assign a propagator to the virtual electron, a vertex factor $ie\gamma^\mu$ at each photon-fermion coupling, and external spinors for the positron and electron.

The core concept here is pair annihilation into photons, which happens through two distinct intermediate states depending on which particle radiates first. The key insight is that both diagrams contribute equally to the total amplitude—one where the electron emits a photon before annihilating, and one where the positron does—so you must draw both and recognize they're related by swapping the role of the two external photons. Writing the amplitude means carefully applying the Feynman rules: assign a propagator to the virtual electron, a vertex factor $ie\gamma^\mu$ at each photon-fermion coupling, and external spinors for the positron and electron.