Eur. Phys. J. C 20, 759-765 (2001)
DOI: 10.1007/s100520100683

Chern-Simons particles with nonstandard gravitational interaction

J. Lukierski^{1, 2}, P.C. Stichel³ and W.J. Zakrzewski<sup>4, 5

1</sup>  Institute for Theoretical Physics, University of Wroclaw, pl. Maxa Borna 9, 50-204 Wroclaw, Poland
²  Departamento de Fisica Teorica, Universidad de Valencia, Av. dr Moliner 50, 46100 Burjasot (Valencia), Spain
³  An der Krebskuhle 21, 33619 Bielefeld, Germany
⁴  Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK
⁵  Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

lukier@ift.uni.wroc.pl
pstichel@gmx.de
W.J.Zakrzewski@durham.ac.uk

(Received: 16 March 2001 / Published online: 13 June 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)

Abstract
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity 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 reparameterization invariant way, to a translational Chern-Simons action. The quantum 2-body problem is described by a nonstandard Schrödinger 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.

© Società Italiana di Fisica, Springer-Verlag 2001