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

TL;DR

This paper explores the topological Chern-Simons term in charge-monopole systems, revealing their interpretation as particles with spin, spinning tops, or higher derivative systems, and discusses their relation to anyons.

Contribution

It introduces new interpretations of the charge-monopole system, including a twistor formulation and a spin description related to spherical geometry.

Findings

Charge-monopole system can be viewed as a particle with fixed spin.

The system can be described as a spinning top with dynamical inertia.

Connections to (2+1)-dimensional anyons are discussed.

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.