Photonic processes in Born–Infeld theory

Abstract

We study the processes of photon–photon scattering and photon splitting in a magnetic field in Born–Infeld theory. In both cases we combine the terms from the tree-level Born–Infeld Lagrangian with the usual one-loop QED contributions, where those are approximated by the Euler–Heisenberg Lagrangian, including also the interference terms. For photon–photon scattering we obtain the total cross-section in the low-energy approximation. For photon splitting we compute the total absorption coefficient in the hexagon (weak field) approximation, and also show that, due to the non-birefringence property of Born–Infeld theory, the selection rules found by Adler for the QED case continue to hold in this more general setting. We discuss the bounds on the free parameter of Born–Infeld theory that may be obtained from this type of processes.