Classical Fields Near Thermal Equilibrium

TL;DR

This paper explores the classical behavior of long-distance modes in quantum fields at thermal equilibrium, emphasizing dissipation and decoherence effects, with implications for scalar and gauge fields.

Contribution

It provides a detailed analysis of the semiclassical dynamics of soft modes in quantum fields, incorporating stochastic effects and dissipation due to thermal hard modes.

Findings

Soft modes exhibit stochastic dynamics similar to Quantum Brownian Motion.

Dissipation and decoherence are significant in the evolution of soft modes.

The framework can be extended to gauge theories.

Abstract

We discuss the classical limit for the long-distance (``soft'') modes of a quantum field when the hard modes of the field are in thermal equilibrium. We address the question of the correct semiclassical dynamics when a momentum cut-off is introduced. Higher order contributions leads to a stochastic interpretation for the effective action in analogy to Quantum Brownian Motion, resulting in dissipation and decoherence for the evolution of the soft modes. Particular emphasis is put on the understanding of dissipation. Our discussion focuses mostly on scalar fields, but we make some remarks on the extension to gauge theories.