Translational Chern–Simons action and new planar particle dynamics.

Lukierski, J.; Stichel, P.C.; Zakrzewski, W.J.

Abstract

We consider a nonstandard D=2+1 gravity described by a translational Chern–Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation Full-size image (<1 K) what implies, after quantization, a nonstandard form of the Schrödinger equation with energy-dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r≤r0) and the scattering states with continuous energy correspond to classical motion for r>r0.

Citation

Lukierski, J., Stichel, P., & Zakrzewski, W. (2000). Translational Chern–Simons action and new planar particle dynamics. Physics Letters B, 484(3-4), 315-322. https://doi.org/10.1016/s0370-2693%2800%2900637-7

• Journal Article Type: Article
• Publication Date: 2000-07
• Journal: Physics Letters B
• Print ISSN: 0370-2693
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 484
• Issue: 3-4
• Pages: 315-322
• DOI: https://doi.org/10.1016/s0370-2693%2800%2900637-7