We perform a perturbative analysis of the Aharonov-Bohm problem to one
loop in a field-theoretic formulation and show that contact interacti
ons are necessary for renormalizability. In general, the classical sca
le invariance of this problem is broken quantum mechanically. There ex
ists, however, a critical point for which this anomaly disappears. (C)
1994 Academic Press, Inc.