Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization

TL;DR

This paper derives the connection dynamics of a reduced 5D Kaluza-Klein theory using Hamiltonian analysis, enabling deparametrization with geometrical degrees of freedom without extra matter fields.

Contribution

It presents a novel Hamiltonian formulation and deparametrization method for the 5D Kaluza-Klein theory in a spherically symmetric setting, relying solely on geometric variables.

Findings

Connection dynamics derived via Hamiltonian analysis.

Deparametrization achieved without additional matter fields.

Physical time and space identified from geometric degrees of freedom.

Abstract

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.