Sobre o problema das cargas conservadas em teorias de calibre

Abstract

In this work, we investigate the integral version of Yang-Mills equations and employ them to solve an open problem in non-abelian gauge theories since 1954: the definition of a gaugeinvariante conserved charge. Throughout this process, we formulate the Lorentz-invariant integral equations of eletromagnetism in vacuum and material media. Additionally, we prove the Stokes theorem, which is fundamental in the connection between integral and differencial versions. We present a new perspective about the conservation of electric charge in electromagnetism as a consequence of a hidden symmetry at the so called loop space. The same symmetry emerges in non-abelian theory and implies in the gauge-invariant conserved charge.