Conserved quantities in non-abelian monopole fields

Details Conserved quantities in non-abelian monopole fields Conserved quantities in non-abelian monopole fields

2009-02-02

arxiv.org/abs/0902.0273v2

Phys.Rev.D79:127701,2009

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, RevTex no figures. An error corrected and a new Section added

Scientific paper

10.1103/PhysRevD.79.127701

Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopole-like field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. It generalizes the fine-tuned inverse-square plus Coulomb potential, found before by McIntosh and Cisneros, and by Zwanziger, for a charged particle in the field of a Dirac monopole. Following Feh\'er, the result is interpreted as describing motion in the asymptotic field of a self-dual Prasad-Sommerfield monopole. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere and Wilczek, a conserved angular momentum is constructed, despite the non-conservation of the electric charge. No Runge-Lenz vector has been found.

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