Anyons: Pseudo-integrability, Symmetry reduction and Semiclassical Spectrum

Details Anyons: Pseudo-integrability, Symmetry reduction and Semiclassical Spectrum Anyons: Pseudo-integrability, Symmetry reduction and Semiclassical Spectrum

1999-06-22

arxiv.org/abs/math-ph/9906018v1

Physics

Mathematical Physics

41 pages, LaTeX, no figures

Scientific paper

At the classical level anyons with harmonic confinement are known to exhibit two important properties namely partial separability and pseudo-integrability. These stem from the fact that this system is locally identical to isotropic oscillator system but differs in the global topology of the phase space. We clarify the meaning of pseudo-integrability and show that it amounts to a definite reduction of the symmetry group. We elaborate on the role of the fundamental group of the phase space and pseudo-intrgrability in the context of periodic orbit theory and obtain evidence of non-exactly known eigenvalues from the semiclassical trace formula. We also discuss an ambiguity regarding the `half period' trajectories suggested by classical modeling and exhibited by the exactly known propagator for two anyons.

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