1999/04/14 by David Hochberg, Hochberg, David, Carmen Molina-Parı́s +7
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical and Theoretical Analysis #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #chao-dyn #cond-mat.stat-mech #hep-th #nlin.CD
paper · pdf · doi:10.48550/arxiv.cond-mat/9904207
5 pages, LaTeX 209, ReV_TeX 3.2. V2: Cosmetic changes to improve handling of Fadeev--Popov ghosts. V3: References updated. This paper has now been superseded and the contents of this paper have now been incorporated into cond-mat/9904215 [Phys. Rev. E60 (1999) 6343-6360]; cond-mat/9904391 [Physica A280 (2000) 437-455]; and cond-mat/9904413 [Phys. Lett. A, in press]
openalex publication_date 1999/04/14 · arxiv created 2000/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classical field theories coupled to stochastic noise provide an extremely powerful tool for modeling phenomena as diverse as turbulence, pattern-formation, and the structural development of the universe itself. In this Letter we sketch a general formalism that maps such systems into a field theory language, and demonstrate how to extract the one-loop physics for an arbitrary classical field theory coupled to Gaussian noise. The amplitude of the noise two-point function serves as the loop-counting parameter and is the analog of Planck's constant hbar in quantum field theory. We define the effective action and the effective potential, and derive a general formula for the one-loop effective potential of a classical field theory coupled to translation-invariant Gaussian noise.