Metric-Induced Principal Symbols in Nonlinear Electrodynamics

TL;DR

This paper introduces a geometric framework for nonlinear electrodynamics using optical metrics, enabling covariant analysis of perturbations and suggesting new laboratory analogue models with nonlinear metamaterials.

Contribution

It presents a novel geometric formulation of nonlinear electrodynamics based on principal symbols and optical metrics, facilitating quantum field theory techniques in nonlinear contexts.

Findings

Reformulation of nonlinear electrodynamics using optical metrics

Covariant divergence description of perturbation evolution

Potential for laboratory analogue models with metamaterials

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.