Introdução à teoria clássica de campos vetoriais

Abstract

Due to the great importance that the classical field theory (CFT) holds in physics, this work presented the foundations of CFT, starting with a review of Lagrangian dynamics and the variational principle of Hamilton, in order to obtain the Euler-Lagrange equations. Subsequently, a brief introduction to tensors was made so that four-vectors could be presented in the context of special relativity. After this extensive review, we obtained the Euler-Lagrange equations for the fields, from which it was possible to deduce the Maxwell equations, which describe the behavior of electric and magnetic fields (and their interactions). This deduction established a connection between CFT and classical electrodynamics (CE), by demonstrating how the Euler-Lagrange equations can be used to derive the laws of CE. Ultimately, through non-abelian groups, we obtain the Yang-Mills tensor, the generalization of electromagnetic fields.