Estudo sobre a transformação de Foldy-Wouthuysen exata para conjunto completo de termos que violam as simetrias CPT/Lorentz na teoria de Dirac

Abstract

The study of the possible candidates to break CPT/Lorentz symmetry is very important nowadays. There are a large number of studies over the last ten years that show the possible experiments that could give the more prominent physical effect to measure external fields that violate fundamental symmetries. An efficient way to study and interpret results of the interaction of the Dirac field with many possible external fields associated with the violation of the CPT/Lorentz symmetries is through the Exact Foldy-Wouthuysen Transformation. In this thesis, we begin with a brief presentation of elements related to the construction of relativistic quantum theory for the description of particles and interactions, as well as the formulation of the Klein-Gordon and Dirac fields. Next, we present the scenario of a Dirac fermion interacting with different external fields that violate the CPT/Lorentz symmetries. It is necessary to perform a Foldy-Wouthuysen Transformation on the Hamiltonian to extract such physical information from it. The Exact Foldy-Wouthuysen transformation method is generalized here. In principle, it is not possible to construct the exact Foldy-Wouthuysen transformation for any Hamiltonian. The transformation conditions are the same, but the involution operator has a new form. We took a particular example and constructed explicitly the new involution operator that allows one to perform the transformation. We treat the case of the Hamiltonian with 160 possible CPT/Lorentz breaking terms, using this new technique. The transformation was performed, and physics analysis of the equations of motion is shown. In addition, we also present a brief perspective on experimental tests in the context of Exact Foldy-Wouthuysen Transformation and future proposals.