Quantização canônica de teorias com violação da simetria de Lorentz

Abstract

This dissertation has as main objective, to study the problem of constructing quantum field theories which are invariant under a referential change, but violate the Lorentz symmetry under changes in the orientation of the experimental apparatus or in the case of displacements with constant speeds of this apparatus. We developed a new procedure for the canonical quantization of a class of Lagrangian involving free charged fields and constant vectors which are responsible for the Lorentz symmetry violation. Through this procedure, it was possible to build operators that satisfy the Poincaré algebra. This result was not obtained by the conventional procedure of canonical quantization. We accomplished the canonical quantization with Lorentz symmetry violation for spinoria and scalar fields as well. We have constructed, for the case of the spinorial field, particles states with energy and spin defined simultaneously. This is another result that was not possible to be obtained using the conventional procedure of canonical quantization. We have presented in the first and third chapter a critica! analysis of the canonical quantization of free fields, showing the essential points for its operation. We have justified the necessity to impose the commutation or anti-commutation relationships in the fields and the necessity to postulate the operators with the sarne functional form of the classical functionals. These analysis allow us to modify the conventional procedure that treat Lagrangians which violate the Lorentz symmetry. As a mathematical base for this whole analysis, we developed in the chapter 2 a systematic method to determine the generator of any continuous transformation.