A sectorial approach to Kaluza-Klein theory

TL;DR

This paper reviews and compares Kaluza-Klein theories, proposing a modified approach where different metric sectors are partially separated with distinct transformation properties, and the cylinder condition is relaxed to differentiate 4-D and 5-D fields.

Contribution

It introduces a novel sectorial Kaluza-Klein model with partial metric separation and relaxed cylinder condition, enhancing the understanding of field localization in higher-dimensional theories.

Findings

Gravitational and electromagnetic fields are confined to a 4-D brane.

Scalar field is confined to the 5-D bulk.

Modified theory offers a new perspective on field separation in higher dimensions.

Abstract

The Kaluza and Klein versions of Kaluza-Klein theory are reviewed and compared. The differences in the field equations of the two theories are related to the transformation properties of the metrics employed. Based on this comparison a modified version of the Kaluza theory is proposed, in which the different sectors of the metric which describe gravitation, electromagnetism and the scalar field are considered to be partially separate entities, with distinct coordinate transformation properties. In addition, the cylinder condition is relaxed, so that it only affects the 4-D sector of the metric. This results in a theory in which the gravitational and electromagnetic fields are restricted to a four-dimensional brane, and the scalar field is restricted to the 5-D bulk.