How Birefringence Arises from Nonlinear Electrodynamics

We analyze the propagation of light signals in the context of nonlinear electrodynamics. As a general feature of the nonlinear theories, the superposition principle is no longer satisfied. In the nonlinear electromagnetic theory, this is because light propagation is influenced by the electromagnetic background. We present a simple derivation of the two light cones (birefringence) that arise if the Lagrangian depends in nonlinear way on the electromagnetic invariants. We formulate the problem as a Sturm-Liouville equation, and, from the algebraic properties of the electromagnetic tensor \(f_{\mu \nu }\) , we obtain the dispersion relations showing that the propagation can be slower or faster than that of light.