Reinterpretação e extensão da teoria unificada de Weyl

Abstract

We revisit Weyl’s unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of geometrization of physics started by Einstein to include the electromagnetic field, H. Weyl developed a new geometry which constitutes a kind of generalization of Riemannian geometry. However, despite its mathematical elegance and beauty, a serious objection was made by Einstein, who considered Weyl’s theory not suitable as a physical theory since it seemed to lead to the prediction of a not yet observed effect, the so-called “second clock effect” . In this thesis, our aim is to discuss Weyl’s proposal anew and examine its consistency and completeness as a physical theory. Finally, we propose new directions and possible conceptual changes in

the original work. As an application, we solve the field equations assuming a Friedmann- Robertson-Walker universe and a perfect fluid as its source. We also present other solutions

for static cases with spherical and cylindrical symmetries. Some aspects of Weyl integral

space-times are also discussed. First, we show that the theory can be casted in the initial- value formulation (the so-called Cauchy problem) and that this form is gauge-invariant.

Second, we obtain a simple cosmological solution, which generalises some cases found in the literature.