Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry

TL;DR

This paper investigates nonlinear vacuum electrodynamics using a first-order formulation, revealing conditions for stable vacua with spontaneous Lorentz symmetry breaking, which could be detectable via external currents or gravity.

Contribution

It introduces a classification of vacua in nonlinear electrodynamics with spontaneous Lorentz symmetry breaking and analyzes their properties using a Hamiltonian approach.

Findings

Existence of stable vacua with nonzero field strength

Classification of vacua into four distinct classes

Potential detectability through external currents or gravity

Abstract

We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Pleba\'nski. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing stationary points in which the field strength acquires a nonzero vacuum expectation value. The associated spontaneous breaking of Lorentz symmetry can in principle be detected by coupling the model to a suitable external current, or to gravity. We show that the possible vacua can be classified in four classes. We study some of their properties, using explicit examples for illustration.