Translational Chern-Simons action and new planar particle dynamics
May, 2000Citations per year
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 Schr\"{o}dinger 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 .Note:
- LateX, 13 pages
- gravitation: action
- Chern-Simons term
- dimension: 3
- particle: nonrelativistic
- Hamiltonian formalism
- quantum mechanics
- Schroedinger equation: solution
- torsion
- energy levels
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