All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized \xi-gauge. The corresponding dispersion relation and tree-level propagator are determined exactly, and some leading-order results are derived. The question of how to include such Lorentz-violating effects into a perturbative quantum-field expansion is addressed. Applications of these results within Lorentz-breaking quantum field theories include the regularization of infrared divergences as well as the free propagation of massive vector bosons.Comment: 12 pages, 1 figur

Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a θ term in a way that has been proposed to provide the correct low-energy effective action for topological insulators (TI). We take the θ term to be piecewise constant in different regions of space separated by a common interface Σ, which will be called the θ boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics, and solutions for some experimental setups have been found, each with its specific configuration of sources. In this work we illustrate a method to construct the GF that allows us to solve the CS modified field equations for a given θ boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar θ boundary but can also be applied for cylindrical and spherical geometries for which the θ boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a pointlike charge interacting with a planar TI, as described by a planar discontinuity in θ, are calculated and successfully compared with previously reported results. We also compute the force between the charge and the θ boundary by two different methods, using the energy-momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.

We consider QED in a constant axial vector background (AEther). Further Lorentz invariance violations (LIV) might occur owing to radiative corrections. The phenomenology of this model is studied, clarifying issues related to the various regularizations employed, with a particular emphasis on the induced photon mass. To this concern, it is shown that in the presence of LIV dimensional regularization may produce a radiatively induced finite photon mass. The possible physical role of the large momentum cutoff is elucidated and the finite temperature radiative corrections are evaluated. Finally, various experimental bounds on the parameters of the model are discussed.

We show for the first time that the induced parity-even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light-like cosmic anisotropy axial-vector or for a time-like one, when in the presence of a bare photon mass.