Small-scale properties of the KPZ equation and dynamical symmetry breaking

A functional integral technique is used to study the ultraviolet or short d istance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gau ssian noise. We apply this technique to calculate the one-loop effective po tential for the KPZ equation. The effective potential is (at least) one-loo p ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renor malizable in 4 or higher space dimensions. This potential is intimately rel ated to the probability distribution function (PDF) for the spacetime avera ged field. For the restricted class of field configurations considered here , the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions. (C) 2001 Elsevier Science B.V. All rights reserved.