OLIVEIRA, R. J. S.; http://lattes.cnpq.br/1949455361433962; OLIVEIRA, Rafael de Jesus dos Santos.
Résumé:
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 .