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Translational Chern--Simons Action and New Planar Particle Dynamics | | J. Lukierski
; P.C. Stichel
; W.J. Zakrzewski
; | | Date: |
12 May 2000 | | Journal: | Phys.Lett. B484 (2000) 315-322 | | Subject: | hep-th gr-qc | | Affiliation: | Wroclaw University), P.C. Stichel (Bielefeld, Germany) and W.J. Zakrzewski (University of Durham | | 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 $H={cal H}(vec{x},vec{p};H)$ 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 $rleq r_0$) and the scattering states with continuous energy correspond to classical motion for $r>r_0$. | | Source: | arXiv, hep-th/0005112 | | Services: | Forum | Review | PDF | Favorites | |
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