DIFFERENTIAL REGULARIZATION OF A NONRELATIVISTIC ANYON MODEL

Differential regularization is applied to a field theory of a nonrelativistic charged boson field phi with lambda (phi*phi)(2) self-interaction and coupling to a statistics-changing U(1) Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the phi*phi*phi phi four-point function, which is the only primitively divergent Green's function, are obtained up to three-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the beta function is investigated. If the renormalization scheme is fixed to agree with a previous one-loop calculation, the two- and three-loop contributions to beta(lambda,e) vanish, and beta(lambda,e) itself vanishes when the ''self-dual'' condition relating lambda to the gauge coupling e is imposed.