Translational Chern-Simons action and new planar particle dynamics

We consider a nonstandard D = 2 + 1 gravity described by a translational Ch ern-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 symmetri es are (local in time) translations and rigid rotations. The phase space Ha miltonian H describing two-body interactions satisfies a nonlinear equation H = H(x,p;H) what implies, after quantization, a nonstandard form of the S chrodinger equation with energy-dependent fractional angular momentum eigen values. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motio n (for the planar distance between two particles r less than or equal to r( 0)) and the scattering states with continuous energy correspond to classica l motion for r > r(0). (C) 2000 Elsevier Science B.V. All rights reserved.