There is a unique Lorentz-violating modification of the Maxwell theory of photons, which maintains gauge invariance, CPT, and renormalizability. Restricting the modified-Maxwell theory to the isotropic sector and adding a standard spin-1 2 Dirac particle p ± with minimal coupling to the nonstandard photon γ, the resulting modified-quantum-electrodynamics model involves a single dimensionless "deformation parameter," κ tr . The exact tree-level decay rates for two processes have been calculated: vacuum Cherenkov radiation p ± → p ± γ for the case of positive κ tr and photon decay γ → p + p − for the case of negative κ tr . From the inferred absence of these decays for a particular high-quality ultrahigh-energy-cosmic-ray event detected at the Pierre Auger Observatory and a well-established excess of TeV gamma-ray events observed by the High Energy Stereoscopic System telescopes, a two-sided bound on κ tr is obtained, which improves by eight orders of magnitude upon the best direct laboratory bound. The implications of this result are briefly discussed.

The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A finite domain of positive and negative values of this Lorentz-violating parameter is determined, in which microcausality and unitarity hold. The main focus of this article is on isotropic modified Maxwell theory, but similar results for an anisotropic nonbirefringent case are presented in the appendix.

There exist two deformations of standard electrodynamics that describe Lorentz symmetry violation in the photon sector: CPT -odd Maxwell-Chern-Simons theory and CPT -even modified Maxwell theory. In this article, we focus on the parity-odd nonbirefringent sector of modified Maxwell theory. It is coupled to a standard Dirac theory of massive spin-1/2 fermions resulting in a modified quantum electrodynamics (QED). This theory is discussed with respect to properties such as microcausality and unitarity, where it turns out that these hold.Furthermore, a priori, the limit of the theory for vanishing Lorentz-violating parameters seems to be discontinuous. The modified photon polarization vectors are interweaved with preferred spacetime directions defined by the theory and one vector even has a longitudinal part. That structure remains in the limit mentioned. Since it is not clear, whether or not this behavior is a gauge artifact, the cross section for a physical process -modified Compton scattering -is calculated numerically. Despite the numerical instabilities occurring for scattering of unpolarized electrons off polarized photons in the second physical polarization state, it is shown that for Lorentz-violating parameters much smaller than one, the modified cross sections approach the standard QED results. Analytical investigations strengthen the numerical computations.Hence, the theory proves to be consistent, at least with regard to the investigations performed. This leads to the interesting outcome of the modification being a welldefined parity-odd extension of QED.

This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gröbner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of Special Relativity that were carried out in the last century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry.

A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentzviolating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the mass of the black hole, is found to have a nonzero probability. These events perhaps allow for a violation of the generalized second law of thermodynamics in the Lorentz-noninvariant theory considered.Physics Letters B 682 (2009) 316 arXiv:0909.0160 [hep-th] (v4)

In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree-level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well-behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.Comment: 32 pages, 4 figures; in version 3.0: added generalized results on optical theore

In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal standardmodel extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classical Lagrangians of the nonminimal SME fermion sector.

In a previous article [1], we established the consistency of isotropic modified Maxwell theory for a finite range of the Lorentz-violating parameter κ tr , which includes both positive and negative values of κ tr . As an aside, we mentioned the existence of a physical model which, for low-energy photons, gives rise to isotropic modified Maxwell theory with a positive parameter κ tr (corresponding to a "slow" photon). Here, we present a related model which gives rise to isotropic modified Maxwell theory with a negative parameter κ tr (corresponding to a "fast" photon). Both models have an identical particle content, photon and Dirac particles, but differ in the type of spacetime manifold considered.