Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua

TL;DR

This paper explores the introduction of Killing-Yano symmetry in phase space, analyzing its symplectic structure and its relation to multipole moments and dynamical symmetries in electromagnetism and continuum mechanics.

Contribution

It introduces Killing-Yano symmetry on phase space and links it to multipole tensors and classical dynamical symmetries, expanding understanding of geometric structures in physics.

Findings

Killing-Yano symmetry defined on phase space.

Relations established between multipole tensors and dynamical symmetry generators.

Analysis performed on flat and constant scalar curvature Riemannian manifolds.

Abstract

In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the $n$-dimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which arise in the expansion of a system of charges and currents, in terms of second-order Killing-Yano tensors in the phase space of classical mechanics. We find some relations between these tensors and the generators of dynamical symmetries like the angular momentum, the mass-inertia tensor, the conformal operator and the momentum conjugate Runge-Lenz vector.