= Tree photon-scattering cancellation in a quadratic Abelian gauge
{title2=$\mathcal M_{\gamma\gamma\to\gamma\gamma}^{\mathrm{tree}}=0$}
The nonlinear <gauge fixing> $\partial\cdot A+\lambda A^2$ produces cubic and quartic <photon> <Feynman vertices>. For physical <photon polarization vectors>, the two-external-leg cubic vertex reduces to a longitudinal internal momentum times the scalar product of the external polarizations. Its exchanged <photon propagator> cancels that momentum squared. Each of the three exchange graphs contributes $+4i\lambda^2(\varepsilon_i\cdot\varepsilon_j)(\varepsilon_k\cdot\varepsilon_l)$, cancelling the corresponding term of the quartic vertex. This vanishing physical <tree-level Feynman diagram> sum does not assert that the <off shell> four-point function vanishes.
Back to article page
