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arXiv · hep-th/9403079

The Higgs model for anyons and Liouville action: Chaotic spectrum, energy gap and exclusion principle

M. Matone
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Abstract

Geodesic completness and self-adjointness imply that the Hamiltonian for anyons is the Laplacian with respect to the Weil-Petersson metric. This metric is complete on the Deligne-Mumford compactification of moduli (configuration) space. The structure of this compactification fixes the possible anyon configurations. This allows us to identify anyons with singularities (elliptic points with ramification $q^{-1}$) in the Poincaré metric implying that anyon spectrum is chaotic for $n\ge 3$. Furthermore, the bound on the holomorphic sectional curvature of moduli spaces implies a gap in the energy spectrum. For $q=0$ (punctures) anyons are infinitely separated in the Poincaré metric (hard-core). This indicates that the exclusion principle has a geometrical intepretation. Finally we give the differential equation satisfied by the generating function for volumes of the configuration space of anyons.

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M. Matone. 1994-03-15. The Higgs model for anyons and Liouville action: Chaotic spectrum, energy gap and exclusion principle. https://doi.org/10.1142/s0217732394001519

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