Um estudo da eletrodinâmica acoplada a férmions e alguns aspectos da mecânica quântica relativística

Abstract

This work seeks to explore the foundations of Classical and Quantum Field Theory, establishing a bridge between Classical Mechanics and modern concepts such as symmetry and gauge invariance. It begins by developing the variational and tensorial formalism required to understand the transition from classical physics to field formulations. Then, electromagnetism is examined from the perspective of a gauge theory, with emphasis on the covariance of Maxwell’s equations and the distinction between global and local symmetries. The study also addresses the gauge principle and its role in quantum mechanics. Finally, relativistic quantum mechanics is introduced through the Klein-Gordon and Dirac equations, discussing their solutions, probability currents, and the famous Dirac Sea interpretation. This study aims to provide a solid conceptual and mathematical foundation for understanding the fundamental theories governing physical interactions in various regimes.