Geometrical Aspects of non-gravitational interactions

TL;DR

This paper proposes a geometric framework for describing non-gravitational forces, specifically electromagnetic interactions, by introducing a proper space-time where these forces are represented as geodesics, similar to gravity in general relativity.

Contribution

It introduces the concept of proper space-time and formulates field equations analogous to Einstein's, providing a geometric interpretation of electromagnetic forces.

Findings

Electromagnetic interactions can be modeled as geodesics in a curved space-time.

The formalism leads to field equations similar to Einstein's equations.

Electromagnetic forces are described geometrically without additional force terms.

Abstract

In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the concept of proper space-time, that allow us to describe this interaction in a way analogous to the one that the general relativity theory does for gravitation. The field equations that define this geometry are similar to the Einstein's equations, where in general, the energy-momentum tensor have information of both, the particle and the external field. In this formalism we consider the particle path as being a geodesic in a curved space-time, and so, the electromagnetic force is understood in a purely geometric way.