Effective potential for the massless KPZ equation
Abstract
In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation (SPDE)) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the oneloop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy Burgers equation), and analyze its behavior in the ultraviolet (shortdistance) regime. When this field theory is subject to white noise we can calculate the oneloop effective potential and show that it is oneloop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the oneloop effective potential for the massless KPZ equation is closely related to that for λφ ^{4} QFT. In particular, we prove that the massless KPZ equation exhibits oneloop dynamical symmetry breaking (via an analog of the ColemanWeinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 June 2000
 DOI:
 10.1016/S03784371(99)006111
 arXiv:
 arXiv:condmat/9904391
 Bibcode:
 2000PhyA..280..437H
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 13 pages, LaTeX 209, ReV_TeX 3.2, three *.eps figures, epsf.sty