Anyons on the sphere: analytic states and spectrum

Abstract

We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial correspondence with the known exact eigenstates on the plane. We also comment on possible connections of this system with integrable systems of the Calogero type.

34 pages, no figures

References in corpus (2)

• Mapping the Calogero model on the Anyon model
• Dimensional reduction on a sphere

Cited by in corpus (10)

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• Shell-shaped atomic gases
• Molecular Impurities as a Realization of Anyons on the Two-Sphere
• Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole
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• Composite anyons on a torus
• Two anyons on the sphere: nonlinear states and spectrum
• Properties of 2D anyon gas
• Dimer problem on a spherical surface
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect