Dynamical supersymmetry of spin particle-magnetic field interaction

Abstract

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\mathbb{N}=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\mathbb{N}=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\mathbb{N}=2$ supersymmetry without Grassmann variable doubling.

23 pages

References in corpus (14)

• Supersymmetric Calogero models by gauging
• Covariant hamiltonian dynamics
• OSp(4|2) Superconformal Mechanics
• Multi-center MICZ-Kepler system, supersymmetry and integrability
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Curved manifolds with conserved Runge-Lenz vectors
• Conserved quantities in non-abelian monopole fields
• SU(2) reduction in N=4 supersymmetric mechanics
• Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• N=4 Supersymmetry and the BPST Instanton
• Dirac Quantization Condition for Monopole in Noncommutative Space-Time
• Dynamal (super)symmetries of monopoles and vortices
• Mechanics and Quantum Supermechanics of a Monopole Probe Including a Coulomb Potential

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• Non-commutative oscillator with Kepler-type dynamical symmetry
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
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