Kaluza's theory in generalized coordinates

TL;DR

This paper extends Kaluza's theory into a 6x6 metric to naturally incorporate magnetic monopoles and derive electrodynamics in generalized coordinates without external forces.

Contribution

It introduces a 6x6 metric extension of Kaluza's formalism to include magnetic monopoles seamlessly in generalized coordinate systems.

Findings

Derived electrodynamics for charged particles without external forces.

Extended Kaluza's formalism to a 6x6 metric.

Provided a natural inclusion of magnetic monopoles.

Abstract

Maxwell's equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work here presented shows how to obtain the electrodynamics for a charged particle in generalized coordinates eliminating the concept of external force. Based on Kaluza's formalism, the one here presented extends the 5x5 metric into a 6x6 space-time giving enough room to include magnetic monopoles in a very natural way.