Metric-Induced Principal Symbols in Nonlinear Electrodynamics

Abstract

We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be recast as a covariant divergence on a curved, field-dependent background, enabling the application of quantum field theory techniques as in Maxwell's theory in curved backgrounds. This geometric reformulation opens a new route for analogue models potentially implementable in laboratory via tailored nonlinear metamaterials.