Electrodynamics with Lorentz-violating operators of arbitrary dimension

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.Comment: 58 pages two-column REVTeX, accepted in Physical Review

Gupta-Bleuler photon quantization in the standard model extension

“…A symmetry under p µ → −p µ reduces the number of independent solutions to four after reinterpretation of the negative energy solutions as positive energy ones. We also note that a factor of p 2 can be extracted from the Tr K 3 term using an argument discussed in [11] involving the dual action of Λ 3 K on the momentum vector. This means that in the massless limit, a factor of p 4 can be factored out of the dispersion relation, in agreement with the results of [11].…”

Lorentz-violating Euler-Heisenberg effective action

“…The effective theory used in these analyses was mainly the Lorentz-violating QED [13], a subset of the minimal standard-model extension [4,5]. For an overview and references on this extended QED, see the review [14] and the incomplete list of works [15][16][17][18][19][20][21][22].…”

Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee field

“…This theoretical framework has inspired a large number of investigations in the last several years, encompassing fermion systems [12][13][14][15][16][17][18][19][20], CPT-probing experiments [21][22][23][24][25][26][27], the electromagnetic CPT-and Lorentzodd term [28]- [41], the CPT-even and Lorentz-odd gauge sector and its interactions with fermions [42][43][44][45][46][47][48][49][50][51], [52][53][54][55][56][57]. Recent investigations involving higher dimensional operators [58][59][60], its possible connections with LV theories [61][62][63][64][65][66], and nonminimal couplings [67][68][69][70]…”