Introdução ao formalismo covariante aplicado ao eletromagnetismo

Abstract

Maxwell’s equations describe the fundamental laws of electromagnetism and are often presented in their vector form. However, when analyzed in the context of Special Relativity, a mathematical inconsistency apparent in the transformations of the electric and magnetic fields is noted. As the laws of Physics must be the same for all inertial frames of reference - principle of Special Relativity, it is necessary to introduce the use of tensors that naturally generalize them to a covariant form. In this way, the electromagnetic field tensor is used, which combines the electric and magnetic fields. This tensor is essential, as it guarantees the mathematical consistency of the laws of electromagnetism in the relativistic context. Therefore, the objective of this work is to present the equations of electromagnetism in its covariant formulation, which consists of expressing the equations using quadrivectors and quadritensors. Maxwell’s equations, in this formalism, represent a generalization to a Minkowski spacetime formulation.