A current algebra approach to the equilibrium classical statistical mechanics and its applications

TL;DR

This paper explores a current algebra framework for classical statistical mechanics, demonstrating its effectiveness in analyzing equilibrium distribution functions, stability, and spectral properties of many-particle systems.

Contribution

It introduces a current algebra approach combined with Bogolubov generating functionals to construct representations and analyze stability in equilibrium classical systems.

Findings

Effective construction of irreducible current algebra representations

Application of the method to analyze stability of equilibrium systems

Discussion of spectral properties related to system stability

Abstract

The non-relativistic current algebra approach is analyzed subject to its application to studying the distribution functions of many-particle systems at the temperature equilibrium and their stability properties. We show that the classical Bogolubov generating functional method is a very effective tool for constructing the irreducible current algebra representations and the corresponding different generalized measure expansions including collective variables transform. The effective Hamiltonian operator construction and its spectrum peculiarities subject to the stability of equilibrium many-particle systems are discussed.