Hamiltonians for Two-Anyon Systems

Abstract

We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction.

Minor corrections; pdfLaTeX, 16 pages

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