arXiv:hep-th/9302116v1 24 Feb 1993 AHARONOV-BOHM SCATTERING, CONTACT INTERACTIONS AND SCALE INVARIANCE* O. Bergman and G. Lozano † Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139 U.S.A. ABSTRACT We perform a perturbative analysis of the Aharonov-Bohm problem to one loop in a field-theoretic formulation, and show that contact interactions are necessary for renormalizability. In general, the classical scale invariance of this problem is broken quantum mechanically. There exists however a critical point for which this anomaly disappears. Submitted to: Physics Letters B Typeset in T E X by Heather Grove CTP#2182 January 1993 * This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069. † Financially supported by the World Laboratory Scholarship Program. 0