How the twofold light cone arises from nonlinear electrodynamics

Abstract

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 electromagnetic theory, this is due to the self-interactions of the field and light propagation is governed by an effective or optical metric. We present a simple derivation of the two light cones that arise if the Lagrangian depends on the electromagnetic invariants in a nonlinear way. Using the algebraic properties of the electromagnetic tensor fμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\\mu \ u }$$\\end{document}, we determine the dispersion relations from the eigenvalues of a Sturm–Liouville equation. It turns out that in the presence of a background field, light propagation can be slower or faster than the one in vacuum. We also derive the corresponding transport vector fields.