Translational Chern--Simons Action and New Planar Particle Dynamics
arXiv:hep-th/0005112 · doi:10.1016/S0370-2693(00)00637-7
Abstract
We consider a nonstandard 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 describing two-body interactions satisfies a nonlinear equation 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 ) and the scattering states with continuous energy correspond to classical motion for .
LateX, 13 pages