Quadratic Forms for Two-Anyon Systems

Abstract: We review the main issues concerning the well-posedness (as suitable self-adjoint operators) of the Hamiltonians of two non interacting anyons, i.e., exotic particles obeying to fractional statistics in two dimensions. We show that such operators can be identified with a one-parameter family of self-adjoint extensions of a suitable symmetric operator with Aharonov-Bohm-like magnetic potential. We also derive the explicit expressions of the corresponding quadratic forms and prove their closure and boundedness from below.
Joint work in progress with M. Correggi.