  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.
