Hamiltonians for two-anyon systems

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 noninteracting 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