Hamiltonian birefringence and Born-Infeld limits
Luca Mezincescu (Department of Physics, University of Miami, P.O. Box 248046, Coral Gables, FL, 33124, USA); Jorge Russo (Departament de Física Cuántica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona, Martí Franquès, 1, Barcelona, 08028, Spain, Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluis Companys, 23, Barcelona, 08010, Spain); Paul Townsend (Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.)
Using Hamiltonian methods, we find six relativistic theories of nonlinear electrodynamics for which plane wave perturbations about a constant uniform background are not birefringent. All have the same conformal strong-field limit to Bialynicki-Birula (BB) electrodynamics, but only four avoid superluminal propagation: Born-Infeld (BI), its non-conformal “extreme” limits (electric and magnetic) and the conformal BB limit. The quadratic dispersion relation of BI is shown to degenerate in the extreme limits to a pair of linear relations, which become identical in the BB limit.