Chern-Simons Particles with Nonstandard Gravitational Interaction

TL;DR

This paper extends a nonrelativistic particle model in (2+1)-gravity to include gauge charges, leading to a modified quantum two-body problem with unique energy level shifts and splittings due to Chern-Simons interactions.

Contribution

It introduces a novel extension of the nonrelativistic particle model to include Abelian and non-Abelian charges coupled via Chern-Simons fields, affecting quantum energy spectra.

Findings

Energy levels are shifted by gauge charges.

Level splitting occurs due to charge interactions.

Numerical results illustrate the spectral modifications.

Abstract

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\"{o}dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels.