Gauge-covariant extensions of Killing tensors and conservation laws

TL;DR

This paper develops a covariant framework for constructing conserved quantities in systems with gauge fields, extending Killing tensors and vectors to include gauge interactions in both classical and quantum contexts.

Contribution

It introduces a manifestly covariant method for deriving gauge-covariant Killing tensors and vectors, applicable to classical and quantum systems with gauge fluxes.

Findings

Constructed gauge-covariant conserved quantities using a covariant phase space approach.

Provided examples demonstrating the application of the method.

Extended the concept of Killing tensors to gauge field environments.

Abstract

In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly covariant procedure, in terms of covariant phase space with a covariant generalization of the Poisson brackets, c.q. quantum commutators. Some examples of this construction are presented.