Monopole Chern-Simons Term: Charge-Monopole System as a Particle with Spin

Abstract

The topological nature of Chern-Simons term describing the interaction of a charge with magnetic monopole is manifested in two ways: it changes the plane dynamical geometry of a free particle for the cone dynamical geometry without distorting the free (geodesic) character of the motion, and in the limit of zero charge's mass it describes a spin system. This observation allows us to interpret the charge-monopole system alternatively as a free particle of fixed spin with translational and spin degrees of freedom interacting via the helicity constraint, or as a symmetric spinning top with dynamical moment of inertia and "isospin" U(1) gauge symmetry, or as a system with higher derivatives. The last interpretation is used to get the twistor formulation of the system. We show that the reparametrization and scale invariant monopole Chern-Simons term supplied with the kinetic term of the same invariance gives rise to the alternative description for the spin, which is related to the charge-monopole system in a spherical geometry. The relationship between the charge-monopole system and (2+1)-dimensional anyon is discussed in the light of the obtained results.

27 pages, relation of twistor form of Chern-Simons term to CP^1 model clarified, discussion of relationship with anyons presented in a separate section, acknowledgements and references added, the version to appear in Nucl. Phys. B

References in corpus (1)

• On the nature of fermion-monopole supersymmetry

Cited by in corpus (34)

• N=4 Supersymmetric Mechanics in Harmonic Superspace
• Superconformal mechanics
• Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
• New variant of N=4 superconformal mechanics
• Covariant hamiltonian dynamics
• Superconformal mechanics and nonlinear supersymmetry
• Particle dynamics on AdS_2 x S^2 background with two-form flux
• Interaction via reduction and nonlinear superconformal symmetry
• Split-Quaternionic Hopf Map, Quantum Hall Effect, and Twistor Theory
• Remarks on Dirac-like Monopole, Maxwell and Maxwell-Chern-Simons Electrodynamics in D=(2+1)
• Curved manifolds with conserved Runge-Lenz vectors
• Symplectic realisation of electric charge in fields of monopole distributions
• Conserved quantities in non-abelian monopole fields
• N=4 superconformal mechanics as a Non linear Realization
• Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Higher order first integrals of motion in a gauge covariant Hamiltonian framework
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Conformal bridge transformation and PT symmetry
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Star-product in the presence of a monopole
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Free conical dynamics: charge-monopole as a particle with spin, anyon and nonlinear fermion-monopole supersymmetry
• Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model
• Dirac's magnetic monopole and the Kontsevich star product
• Generalized N = 2 Super Landau Models
• Localizability, gauge symmetry and Newton-Wigner operator for massless particles
• BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor
• Complex angular momenta approach for scattering problems in the presence of both monopoles and short range potentials
• Factorization method and the supersymmetric monopole harmonics
• 2T Physics, Scale Invariance and Topological Vector Fields
• Alternative Description of Magnetic Monopoles in Quantum Mechanics
• Disappearance of Schwinger's string at the charge - monopole "molecule"