Métodos de quantização aplicados à partículas supersimétricas

Abstract

In this Masters dissertation, some methods of quantization applied to the supersymmetric particle model were studied. Emphasis was given to two specific methods, the covariant quantization of Gupta-Bleuler, which is a method applied to systems that have constraints and the quantization by Feynman path integrals, a more elegant and also more powerful process of making the transition from classical to the quantum level of a theory with or without constraints. A brief discussion was made on supersymmetric particle theory, which uses commutative variables to describe its motion in space-time and anti-commutative variables of Grassmann’s algebra to describe spin degrees of freedom. Among the most interesting results obtained from the quantization of the model by the Gupta-Bleuler method is the identification of Grassmann’s algebra with the Clifford’s one at the quantum level and the massless Dirac equation. In the path integral approach, two systems were studied, namely the relativistic spinless particle, which quantization led to the Klein-Gordon propagator, and the supersymmetric particle spinning, which quantization led to the propagator of the Dirac equation. All these results, in both quantization schemes, are in total agreement with the already well established theories in the literature on these subjects.