Eur. Phys. J. C 20, 759-765 (2001)
DOI: 10.1007/s100520100683
Chern-Simons particles with nonstandard gravitational interaction
J. Lukierski1, 2, P.C. Stichel3 and W.J. Zakrzewski4, 51 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