Nonrenormalizability of the classical statistical approximation

2014/02/07 by Thomas Epelbaum, François Gelis, Francois Gelis +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Approximation error #Approximation theory #Born–Huang approximation #Field (mathematics) #High frequency approximation #High-Energy Particle Collisions Research #Linear approximation #Mathematical analysis #Mathematics #Muffin-tin approximation #Physics #Quantum #Quantum field theory #Quantum mechanics #Scattering #Scheme (mathematics) #Spouge's approximation #Statistical Mechanics and Entropy #Statistical physics #hep-ph #hep-th #nucl-th

paper · pdf · doi:10.1103/physrevd.90.065029

published as Phys. Rev. D 90, 065029 (2014) · 31 pages, 29 figures

arxiv created 2014/02/07 · openalex publication_date 2014/09/23 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in quantum field theory. Although the ultraviolet power counting in this approximation scheme is identical to that of the unapproximated quantum field theory, this approximation is not renormalizable. The leading cause of this nonrenormalizability is the breakdown of Weinberg's theorem in this approximation. We also discuss some practical implications of this negative result for simulations that employ this approximation scheme, and we speculate about a possible modification of the classical statistical approximation in order to systematically subtract the leading residual divergences.

Citations

• Universal attractor in a highly occupied non-Abelian plasma
• Renormalized Finite Temperature theory from the 2PI Effective Action
• Problems with lattice methods for electroweak preheating
• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• Nonperturbative renormalization for 2PI effective action techniques
• The evolving Glasma
• Nonlinear amplification of instabilities with longitudinal expansion
• High energy factorization in nucleus-nucleus collisions. II. Multigluon correlations
• The Color Glass Condensate
• Effective action for composite operators
• TheSMatrix in Quantum Electrodynamics
• 2PI nonequilibrium versus transport equations for an ultracold Bose gas
• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. II. Diagrammatic Formulation