On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers

2002/12/13 by A.H. Mueller, A. H. Mueller, D. Son +1 · 2 citations
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Gas Dynamics and Kinetic Theory #High-Energy Particle Collisions Research #hep-ph

paper · pdf · doi:10.1016/j.physletb.2003.12.047

published as Phys.Lett. B582 (2004) 279-287 · 15 pages, 7 figures

arxiv created 2002/12/13 · openalex publication_date 2004/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We consider a system made up of excitations of a neutral scalar field, φ, having a λφ4 interaction term. Starting from an ensemble where the occupation number f is large, but λf is small, we develop a classical field theory description of the evolution of the system toward equilibrium. A Boltzmann equation naturally emerges in this description and we show by explicit calculation that the collision term is the same as that coming from elastic scattering. This shows the equivalence of a Boltzmann equation description and a classical field theory description of the same system, at least to the leading orders in the occupation number.

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