Stable Magnetic Lorentz-Violating Vacua in Gauge-Invariant Nonlinear Electrodynamics

TL;DR

This paper explores stable Lorentz-violating magnetic vacua in gauge-invariant nonlinear electrodynamics, identifying parameter regions for physically admissible vacua and discussing implications for symmetry breaking and causality.

Contribution

It introduces a Hamiltonian framework for analyzing Lorentz-violating vacua in specific nonlinear electrodynamics models and clarifies conditions for stability and symmetry breaking.

Findings

Stable magnetic Lorentz-violating vacua exist in certain parameter regions.

Hamiltonian boundedness alone does not guarantee spontaneous Lorentz symmetry breaking.

Conditions for stability relate to strong-field causality criteria.

Abstract

We investigate gauge-invariant nonlinear electrodynamics in the Pleba\'nski first-order Hamiltonian formulation, taking the single-invariant potential $\hat V(P)$ as the primary object. Our focus is on the existence of stable Lorentz-violating magnetic vacua. For three explicit two-parameter models -- rational asymmetric, logarithmic, and exponential -- we determine the regions of parameter space in which nontrivial constant electromagnetic vacua are compatible with an effective Hamiltonian bounded from below and a positive-semidefinite Hessian. In all three cases, physically admissible Lorentz-violating vacua are realized in the magnetic branch. We further discuss the electric branch and several additional one-parameter models, illustrating that Hamiltonian boundedness by itself does not ensure spontaneous Lorentz symmetry breaking. We also comment on how the symmetry-breaking conditions are related to known strong-field causality criteria.