MATEUS, A. E.; http://lattes.cnpq.br/1713329736377595; MATEUS, Anderson Evangelista.
Resumo:
One of the theories that has been taking shape in recent years, both in theoretical and
experimental aspects, is the idea that Lorentz’s symmetry can be violated in the high
energy regime, on the Planck scale. It seems that on this scale, the physics we know,
based on the Standard Model and the Theory of Relativity, should be unified in a theory
of quantum gravity. From this scenario, the possibility arises that the Lorentz symmetry,
fundamental in Physics, may be broken on this scale of energy. Since the caliber symmetry
breaking mechanism that occurs spontaneously and that explains, for example, mass
creation in a boson theory, is known, it is possible that Lorentz symmetry can also be
broken spontaneously . On the other hand, another phenomenon that generates discussions,
but which is more accepted within the community is the possibility that particles that
interact with a flutuating quantum field can perform a random movement similar to the
observed by Robert Brown in the 19th century with pollen grains. This movement is
sometimes called the quantum brownian motion (QBM). It has been shown that QBM can
occur in a flat geometry or in a time dependent one. So, a good question to ask is what is
the effect of Lorentz’s symmetry breaking for the quantum brownian motion performed by
a point particle? It is this question that we wish to answer in this thesis. To investigate
this, it is necessary that the equations that describe this type of movement be modified by
introducing terms that carry the Lorentz symmetry violation.