Implicações da quebra de Lorentz na mecânica quântica não-relativística

Abstract

This work is dedicated to fundamental concepts of nonrelativistic quantum mechanics. A summary of the laws of quantum cinematics and quantum dynamics is presented. The latter involves the propagation amplitude known as the propagator, which describes quantum motion of a nonrelativistic particle between two points. The properties of the

propagator are also discussed in this context. Subsequently, the text explains the single- and double-slit experiments, which are basic experiments demonstrating the essential

behavior of a quantum object. The observations made in these experiments as well as the conclusions on the behavior of a quantum particle deduced from them are summarized. The main goal of this master thesis is to incorporate a possible manifestation of Lorentz symmetry violation into the propagator, i.e., to derive a modied propagator. The focus is on a relatively simple contribution from the Standard-Model Extension (SME). The SME is an eective, theoretical framework that parameterizes all the possibilities of Lorentz invariance violation in the context of eld theory. The modied propagator is employed to obtain the interference pattern for the double-slit experiment with pointlike slits. The result is that the interference pattern remains unchanged for the particular contribution of the SME that is studied. The conclusions of this discovery are discussed and proposals for more sophisticated analyses are made, as well.