Conserved quantities in non-abelian monopole fields

Abstract

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 Fehér, 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.

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

References in corpus (7)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Cold atom dynamics in non-Abelian gauge fields
• Covariant hamiltonian dynamics
• Monopole Chern-Simons Term: Charge-Monopole System as a Particle with Spin
• Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole
• Rotation Symmetry and Nonabelian Berry Potential

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• Curved manifolds with conserved Runge-Lenz vectors
• Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Higher order first integrals of motion in a gauge covariant Hamiltonian framework
• N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole Background
• Generalized five-dimensional Kepler system, Yang-Coulomb monopole and Hurwitz transformation
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• Dynamical supersymmetry of spin particle-magnetic field interaction
• Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
• Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
• Extended supersymmetry and its applications in quantum mechanical models associated with self-dual gauge fields