Gravitação e o campo de Proca

Abstract

This dissertation constitutes a study on Weyl’s unified theory, which attempted in 1918 to unify electromagnetism and gravitation into a single theory. Initially, we present in detail the way in which this theory was constructed. Then, trying to make it complete and consistent with Weyl’s original spirit, that is, that of a theory exhibiting a new symmetry, namely, a gauge symmetry, we present a new proposal to make the metric tensor and the Weyl field invariant quantities with respect to gauge transformations. This allows us to develop a gauge invariant notion of proper time, besides allowing to describe the coupling of the geometric fields (gravitational and electromagnetic) with the matter fields. With this in mind, it was necessary to modify and reinterpret Weyl’s original theory. In this way, we obtain a new kind of alternative theory of gravity. An important aspect that we emphasize in this dissertation is the reinterpretation (inWeyl’s original theory) of the field responsible for the geometry of parallel transport as being formally identical to a massive vector field, which takes us back to the old theory developed by the Romanian physicist Alexandru Proca, developed in 1936, in the context of a theory of nuclear interactions, somewhat anticipating Hideki Yukawa’s later theory for explaining strong nuclear forces. Thus, we dedicate part of this dissertation to the study of the Proca field in several different situations: in Minkowski’s space-time, in the theory of general relativity, as well as in Weyl’s invariant theory.