Estudo sobre a Transformação Foldy-Wouthuysen Exata para termos que violam as simetrias CPT/Lorentz na Teoria de Dirac

Abstract

In this work, a brief review of basic elements and concepts related to relativistic quantum theory and Dirac representation is presented, and then, the formulations of the Klein-Gordon and Dirac fields are introduced. Subsequently, the Dirac fermion is considered interacting with different external fields that violate the fundamental symmetries, including CPT and Lorentz. A very efficient approach to extract physical information from the Hamiltonian is to perform a Foldy-Wouthuysen transformation on it. In addition to the perturbative Foldy-Wouthuysen Transformation, there is the exact version, which is not based on power series in the parameter 1/m. The use of this technique is shown in a didactic form, since it allows to work and to investigate any case of interaction of external fields with the Dirac field. A new approach is developed to study all the cases for which the exact transformation is not allowed, through a generalization of the method and the development of a new involution operator. Furthermore, a brief perspective on experimental tests is also presented, considering the complete EFWT scenario, including all possible cases that violate the CPT and Lorentz symmetries in the Dirac equation.