In previous work we have developed a general method for casting a classical
field theory subject to Gaussian noise (that is, a stochastic partial diff
erential equation (SPDE)) into a functional integral formalism that exhibit
s many of the properties more commonly associated with quantum field theori
es (QFTs). In particular, we demonstrated how to derive the one-loop effect
ive potential. In this paper we apply the formalism to a specific field the
ory of considerable interest, the massless KPZ equation (massless noisy Bur
gers equation), and analyze its behavior in the ultraviolet (short-distance
) regime. When this field theory is subject to white noise we can calculate
the one-loop effective potential and show that it is one-loop ultraviolet
renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet
renormalizable in higher dimensions. We show that the one-loop effective p
otential for the massless KPZ equation is closely related to that for lambd
a phi(4) QFT. In particular, we prove that the massless KPZ equation exhibi
ts one-loop dynamical symmetry breaking (via an analog of the Coleman-Weinb
erg mechanism) in 1 and 2 space dimensions, and that this behavior does not
persist in 3 space dimensions. (C) 2000 Elsevier Science B.V. All rights r
eserved.