A quebra da invariância de Lorentz na eletrodinâmica quântica através de um espaço-tempo intrinsecamente anisotrópico.

Abstract

In this work, we considered the proposition that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler's geometry, since Finsler's spacetime is intrinsically anisotropic and naturally induces Lorentz invariance violation (LIV). With the focus on quantum electrodynamics (QED), in which the electromagnetic and fermionic sectors are described in locally Minkowski spacetime, the lagrangian density explicitly presented for the case of the electromagnetic eld, is compatible with the standard model extension (SME). The Lorentz-violating Maxwell equations invariance as well as the electromagnetic wave equation are obtained, and the plane wave solutions for the electromagnetic wave gives the dispersion relation that characterizes the lightcone, where it can be narrowed or enlarged from According to the Finsler's spacetime parameter LIV. The speed of light may depend on the direction of light, becoming superluminal or subluminal, and such LIV e ects can be seen as influences of an anisotropic source on the electromagnetic wave. An anisotropic space-time constraint is made from observations of gamma-ray bursts (GRBs), so that the speed of light is subluminal and dependent on energy. In addition, the birefringence of light does not appear during the process of this model. For the case of the fermionic sector, is investigated the possibility of the induction of the Finsler electromagnetic term by the quantum correction method in four dimensions, which leads to a Finsler electromagnetic term dependent on a divergent part that breaks the Lorentz invariance .