Abstract
In the presence of Lorentz Symmetry Violation (LSV) associated with the Standard-Model Extension (SME), we have recently shown the non-conservation of the energy-momentum tensor of a light-wave crossing an Electro-Magnetic (EM) background field even when the latter and the LSV are constant. Incidentally, for a space-time dependent LSV, the presence of an EM field is not necessary. Herein, we infer that in a particle description, the energy non-conservation for a photon implies violation of frequency invariance in vacuo, giving rise to a red or blue shift. We discuss the potential consequences on cosmology.
Highlights
The Standard-Model (SM) describes through a Lagrangian three interactions among fundamental particles: ElectroMagnetic (EM), weak and strong
In two recent works [5,6] on the Standard-Model Extension (SME), we have considered violations of Lorentz Symmetry (LoSy), differing in the handedness of the Charge conjugation-Parity-Time reversal (CPT) symmetry and in whether considering the impact of photinos on photon propagation
We have shown the emergence of birefringence
Summary
The Standard-Model (SM) describes through a Lagrangian three interactions among fundamental particles: ElectroMagnetic (EM), weak and strong. For the CPT-odd classes (kαAF breaking vector) associated with the Carroll– Field–Jackiw (CFJ) model, the dispersion relations (DRs) and the Lagrangian show for the photon an effective mass, gauge-invariant, and proportional to |kAF|. For the CPT-even classes (kFανρσ breaking tensor), when the photino is considered, the DRs display a massive behaviour inversely proportional to a coefficient in the Lagrangian and to a term linearly dependent on kFανρσ. We have shown the emergence of birefringence For both CPT sectors, we have pointed out the non-conservation of the photon energy-momentum tensor in vacuo [6]. Thereby, there is an explicit xα dependence at the level of the Lagrangian This determines a source of energy-momentum non-conservation, according to the Noether theorem. This guarantees gauge invariance of the action and, in a connected space, kAF may be expressed as the four-gradient of a scalar function
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