Análise clássica e quântica de sistemas com simetrias locais e suas aplicações

Abstract

After more than 60 years of its initial development, the Dirac-Bergmann method for hamiltonization of constrained systems is still a powerful tool for analysis and investigation of modern theoretical models. As a motivation, we shall present several models where the method is applied, then we will describe it in details, with a sequence of steps. The main objective of this work is to provide distinct applications of the Dirac method, including the search for local symmetries of singular theories, the construction of the Magueijo-Smolin doubly special relativity proposal, the formulation of classical mechanics with reparametrization invariance and its quantization and finally, we discuss a semiclassical mechanical model that produces the Dirac equation through quantization.