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Effective potential for the massless KPZ equation

Author

Listed:
  • Hochberg, David
  • Molina-Parı́s, Carmen
  • Pérez-Mercader, Juan
  • Visser, Matt

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 one-loop 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 (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 potential for the massless KPZ equation is closely related to that for λφ4QFT. In particular, we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman–Weinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.

Suggested Citation

  • Hochberg, David & Molina-Parı́s, Carmen & Pérez-Mercader, Juan & Visser, Matt, 2000. "Effective potential for the massless KPZ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 437-455.
    • Handle: RePEc:eee:phsmap:v:280:y:2000:i:3:p:437-455
    DOI: 10.1016/S0378-4371(99)00611-1
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