Srednicki — Quantum Field Theory · Problem 67.1

Canonical Quantization of Scalar Fields — Mark Srednicki

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

Problem

Show explicitly that the tree-level e~+e~−→γγ\tilde{e}^+\tilde{e}^- \to \gamma\gamma scattering amplitude in scalar electrodynamics, T=−e2[4(k1⋅ε1′)(k2⋅ε2′)m2−t+4(k1⋅ε2′)(k2⋅ε1′)m2−u+2(ε1′⋅ε2′)],\mathcal{T} = -e^2\left[\frac{4(k_1\cdot\varepsilon_{1'})(k_2\cdot\varepsilon_{2'})}{m^2-t} + \frac{4(k_1\cdot\varepsilon_{2'})(k_2\cdot\varepsilon_{1'})}{m^2-u} + 2(\varepsilon_{1'}\cdot\varepsilon_{2'})\right], vanishes if ε1′μ\varepsilon^\mu_{1'} is replaced with k1′μk_1^{\prime\mu}.

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