Geometric and covariant interpretation and formulation of electromagnetism using gauge theories and the notion of tangent fibrates

Abstract

The objective of this work is to reformulate the electromagnetic theory with new ideas using geometric concepts, such as differential manifold, tangent bundles, Lie algebra, all within a Gauge theory with U(1) symmetry (unitary transformation) from a more mathematical perspective and not experimental. Within the conclusions we have that: the Faraday curvature tensor rμυ is equal to the electromagnetic field tensor Fμυ when there is an affine connection with local symmetry U (1). Thus, it can be said that the electromagnetic fields are a consequence of the fact that there is a curvature in differential manifold internal to the charge density quadrivector, the charge lives in the 4-dimensional space-time of the Minkowski theory, but the charge has an internal space associated with a affine connection given by Aμ , when in that internal space there is curvature then an electric and magnetic field are reflected in the Minkowski space of time or the real space where all physical objects live and for that reason we can measure the electric field and magnetic. Only when there is curvature in that internal space does an electric field E ⃗ and a magnetic field B ⃗ manifest in our physical world.