Gauge theories and spontaneous symmetry breaking

Abstract

[en] In this work, we present a formulation of gauge theories from a mathematical perspective, through bundles and connections on them. We begin by providing the necessary background in differential geometry, covering topics such as Lie groups, Lie algebras, principal bundles and their connection 1 − forms. Then, we examine how classical Yang-Mills theories, a type of gauge theories, can be interpreted using the presented concepts. In particular, we focus on the explanation of the electroweak interaction as a Yang-Mills theory, following the Standard Model of particle physics. Finally, we study some of the problems of this formalism and the way they can be solved via the Higgs mechanism, based on the notion of spontaneous symmetry breaking.