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

Dumitru Baleanu·V. M. Dubovik·S. Misicu
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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.

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Dumitru Baleanu, V. M. Dubovik, S. Misicu. 1999-08-18. Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua. https://arxiv.org/abs/math-ph/9806011

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