Higher order first integrals of motion in a gauge covariant Hamiltonian framework

TL;DR

This paper explores higher order symmetries and conserved quantities in a gauge covariant Hamiltonian framework, emphasizing the role of Killing-Yano tensors and providing explicit examples with Runge-Lenz type integrals.

Contribution

It extends the covariant phase-space approach to include gauge fields and scalar potentials, highlighting the significance of Killing-Yano tensors in higher order integrals of motion.

Findings

Identified higher order symmetries in gauge covariant systems.

Extended phase-space formalism to include gauge fields and potentials.

Explicit examples of Runge-Lenz type conserved quantities.

Abstract

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some non-trivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.