Non-renormalizability of the classical statistical approximation

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 non-renormalizability 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.

31 pages, 29 figures

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Cited by in corpus (25)

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• Nonequilibrium fixed points in longitudinally expanding scalar theories: infrared cascade, Bose condensation and a challenge for kinetic theory
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• Back-reaction on background fields: a coherent state approach
• Nonthermal Fixed Points in Quantum Field Theory Beyond the Weak-Coupling Limit
• Evolution to the Quark-Gluon Plasma
• Spectral functions from the real-time functional renormalization group
• Early quark production and approach to chemical equilibrium
• Initial State Quantum Fluctuations in the Little Bang
• Time evolution of linearized gauge field fluctuations on a real-time lattice
• Properties of the Boltzmann equation in the classical approximation
• Kinetic theory of a longitudinally expanding system of scalar particles
• Attractive vs. repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories
• Bubble velocities and oscillon precursors in first-order phase transitions
• Comments on the adiabatic theorem
• Schwinger Mechanism with Stochastic Quantization
• Quantum corrections to the Classical Statistical Approximation for the expanding quantum field
• The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics
• Thermalization of gluons in spatially homogeneous systems
• Initial state in relativistic nuclear collisions and Color Glass Condensate
• Shear viscosity of the ${\Phi }^4$ theory from classical simulation
• Renormalization out of equilibrium in a superrenormalizable theory
• Long and short distance behavior of the imaginary part of the heavy-quark potential
• Early Time Dynamics and the Bulk
• Kinetic theory of a longitudinally expanding system