Srednicki — Quantum Field Theory · Problem 67.2

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · ward-identity-spinor-qed-compton

Problem

Show explicitly that the tree-level

e^+e^- \to \gamma\gamma

scattering amplitude in spinor electrodynamics,

\mathcal{T} = e^2\, \overline{v}_2\left[\not{\varepsilon}_{2'}\left(\frac{-\not{p}_1 + \not{k}'_1 + m}{m^2-t}\right)\not{\varepsilon}_{1'} + \not{\varepsilon}_{1'}\left(\frac{-\not{p}_1 + \not{k}'_2 + m}{m^2-u}\right)\not{\varepsilon}_{2'}\right]u_1 ,

vanishes if

\varepsilon^\mu_{1'}

is replaced with

k_1^{\prime\mu}