Classical fields method for a relativistic interacting Bose gas

TL;DR

This paper develops a classical fields approach for relativistic interacting Bose gases at finite temperatures, emphasizing the importance of a momentum cut-off to separate classical and quantum effects, and applies it to thermodynamics with Klein-Gordon dynamics.

Contribution

It introduces a classical fields method tailored for relativistic Bose gases, incorporating a momentum cut-off to distinguish classical and quantum regimes, and demonstrates its application to thermodynamic properties.

Findings

Effective classical description at low temperatures

Role of momentum cut-off in separating classical and quantum effects

Application to thermodynamics of Klein-Gordon Bose field

Abstract

We formulate a classical fields method for description of relativistic interacting bosonic particles at nonzero temperatures. The method relays on the assumption that at low temperatures the Bose field can be described by a c-number function. We discuss a very important role of the cut-off momentum which divides the field into dominant classical part and a small quantum correction. We illustrate the method by studying a thermodynamics of relativistic Bose field which dynamics is governed by the Klein-Gordon equation with $\lambda \psi^4$ term responsible for interactions.