Electrodynamics with Lorentz-violating operators of arbitrary dimension

TL;DR

This paper develops a comprehensive theoretical framework for analyzing photon behavior under Lorentz and CPT violation, classifying all gauge-invariant terms of arbitrary dimension, and applies it to astrophysical and laboratory tests.

Contribution

It introduces a complete classification of Lorentz- and CPT-violating operators of any dimension in photon electrodynamics, including their effects on dispersion and birefringence, and connects theory with experimental constraints.

Findings

Derived covariant dispersion relations for Lorentz-violating photons.

Set new bounds on Lorentz violation coefficients from gamma-ray burst data.

Predicted frequency shifts in cavity experiments due to Lorentz-violating effects.

Abstract

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentz- and CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete characterization of the coefficients for Lorentz violation for all mass dimensions via a decomposition using spin-weighted spherical harmonics. The resulting nine independent sets of spherical coefficients control birefringence, dispersion, and anisotropy. We discuss the restriction of the general theory to various special models, including among others the minimal Standard-Model Extension, the isotropic limit, the case of vacuum propagation, the nonbirefringent limit, and the vacuum-orthogonal model. The transformation of the spherical coefficients for Lorentz violation between the laboratory frame and the standard Sun-centered frame is provided. We apply the results to various astrophysical observations and laboratory experiments. Astrophysical searches of relevance include studies of birefringence and of dispersion. We use polarimetric and dispersive data from gamma-ray bursts to set constraints on coefficients for Lorentz violation involving operators of dimensions four through nine, and we describe the mixing of polarizations induced by Lorentz and CPT violation in the cosmic-microwave background. Laboratory searches of interest include cavity experiments. We present the theory for searches with cavities, derive the experiment-dependent factors for coefficients in the vacuum-orthogonal model, and predict the corresponding frequency shift for a circular-cylindrical cavity.