Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation

TL;DR

This paper explores hidden symmetries in gauge covariant Hamiltonian systems, emphasizing the role of Stackel-Killing tensors, and introduces a reduction and unfolding procedure to analyze these symmetries.

Contribution

It introduces a novel reduction and unfolding method to analyze hidden symmetries in gauge covariant Hamiltonian formulations, highlighting the role of Stackel-Killing tensors.

Findings

Identification of hidden symmetries via gauge covariant equations

Development of a staged reduction and unfolding procedure

Connection between gauge transformations and scalar potentials

Abstract

Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original phase space to another one in which the symmetries are divided out. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.