Lukierski, J., Stichel P.C. & Zakrzewski, W.J. (2000). Translational Chern–Simons action and new planar particle dynamics. Physics Letters B 484
Author(s) from Durham
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.