QED with external field: Hamiltonian treatment for anisotropic medium formed by the Lorentz-non-invariant vacuum

TL;DR

This paper develops a Hamiltonian formalism for nonlinear QED in an external Lorentz-noninvariant field, treating it as an anisotropic medium, and explores the resulting modified electrodynamics and photon properties.

Contribution

It introduces a Hamiltonian approach to nonlinear QED in anisotropic media, defining new generators and energy-momentum tensors, and analyzing photon magnetic moments.

Findings

Hamiltonian formalism for nonlinear QED in anisotropic medium

Modified energy-momentum tensor and conserved quantities

Photon magnetic moment influences angular momentum evolution

Abstract

Nonlinear electrodynamics, QED included, is considered against the Lorentz-noninvariant external field background, treated as an anisotropic medium. Hamiltonian formalism is applied to electromagnetic excitations over the background, and entities of electrodynamics of media, such as field inductions and intensities, are made sense of in terms of canonical variables. Both conserved and nonconserved generators of space-time translations and rotations are defined on the phase space, and their Hamiltonian equations of motion and Dirac bracket relations, different from the Poincar\'e algebra, are established. Nonsymmetric, but--in return--gauge-invariant, energy-momentum tensor suggests a canonical momentum density other than the Poynting vector. A photon magnetic moment is found to govern the evolution of the photon angular momentum. It is determined by the antisymmetric part of the energy-momentum tensor.