Monopole Chern–Simons term: charge–monopole system as a particle with spin Original Research Article

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 chargeʹs 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.