DIFFERENTIAL REGULARIZATION OF A NONRELATIVISTIC ANYON MODEL

Differential regularization is applied to a field theory of a nonrelat ivistic charged boson field phi with lambda (phiphi)(2) self-interact ion and coupling to a statistics-changing U(1) Chern-Simons gauge fiel d. Renormalized configuration-space amplitudes for all diagrams contri buting to the phiphi*phi phi four-point function, which is the only p rimitively divergent Green's function, are obtained up to three-loop o rder. The renormalization group equations are explicitly checked, and the scheme dependence of the beta function is investigated. If the ren ormalization scheme is fixed to agree with a previous one-loop calcula tion, the two- and three-loop contributions to beta(lambda,e) vanish, and beta(lambda,e) itself vanishes when the ''self-dual'' condition re lating lambda to the gauge coupling e is imposed.