Differential regularization of a nonrelativistic anyon model.

Differential regularization is applied to a field theory of a non-relativistic charged boson field φ with λ(φ∗φ)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 φφφφ 4-point function, which is the only primitively divergent Green’s function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the β-function is investigated. If the renormalization scheme is fixed to agree with a previous 1loop calculation, the 2and 3-loop contributions to β(λ, e) vanish, and β(λ, e) itself vanishes when the “self-dual” condition relating λ to the gauge coupling e is imposed. CTP #2216 hep-th/9306117 June 1993 This research is supported in part by D.O.E. contract DE-AC02-76ER03069, N.S.F. Grant PHY/9206867 and by CICYT (Spain) under Grant AEN90-0040.