Einstein-Cartan-Maxwell Theory with Scalar Field through a Five-Dimensional Unification

TL;DR

This paper proposes a modified Kaluza-Klein framework that unifies gravity and electromagnetism through torsion fields in a five-dimensional space, incorporating a scalar field without inducing torsion in four dimensions.

Contribution

It introduces a novel five-dimensional unification model where torsion fields emerge naturally, extending Einstein-Cartan-Maxwell theory with scalar field considerations.

Findings

Torsion fields arise from symmetry breaking in five-dimensional space.

Electromagnetic field strength is represented by torsion's fifth component.

Scalar field does not induce torsion in four-dimensional space.

Abstract

A modification of Kaluza-Klein theory is proposed in which, as a result of a symmetry breaking, five-dimensional space-time is partially parallelized implying the appearance of torsion fields. A naturally chosen action functional leads to the Einstein-Cartan-Maxwell theory where the electromagnetic field strength is represented by the fifth component of the torsion 2-form. Incorporation of a scalar field reveals that four-dimensional space-time torsion is not induced by the scalar field.