Eletrodinâmica de Maxwell modificada por termo CPT-par de altas derivadas e violação da simetria de Lorentz

Abstract

The Standard Model Extension (MPE), proposed in 1998 by Kostelecky and Colladay, shares several properties of the Standard Model already known, such as renormalizability, energy and momentum conservation and gauge symmetry, but does not preserve the Lorentz symmetry, with possibility of violating CPT symmetry as well. The gauge sector of the MPE contains a CPT-even term and a CPT-odd one. The object of study in this dissertation is only the CPT-even one, represented by the tensor (kF )κλµν , which contains 19 independent components. In the third chapter, we present a review of Maxwell’s electrodynamics modified by the non birefringent CPT-even term, being the tensor (kF )κλµν reduced to the symmetric tensor, Dαλ. The parameterization of this tensor is given by (CαBλ + CλBα) /2, where Bα and Cλ are two 4-vectors. In the fourth chapter, as a prototype of electromagnetic theory with high derivatives, we study the Podolsky electrodynamics, analyzing some of its main features. We analyze the equations of motion for the potential, finding the solution for the electrostatic potential by means of the Green´s method. Then, we calculate the Feynman´s propagator, whose poles provide the dispersion relations of the theory, and allow to assess its causality, stability and unitarity. In the fifth chapter of this dissertation, we examined an electrodynamics with high order derivatives, containing a term of type ∂σFσβ∂λFλαDβα, where Dβα is a Lorentz symmetry violation tensor, symmetric and CPT-par. This term may or may not contain the Podolsky term, associated with the trace of Dνµ tensor. Using an appropriate parameterization, Dνµ = 1/2 (CνBµ + CµBν) , we calculate the Feynman propagator, achieving the dispersion relations of this theory, and examining the causality of several sectors. We finish presenting the classical solutions for this theory obtained by the Green´s method.