Field Theoretic Formulation of Kinetic theory: I. Basic Development

TL;DR

This paper develops a field theoretic formulation of kinetic theory for classical particles, enabling a self-consistent perturbation expansion to study ergodic-nonergodic transitions, with detailed implementation for Smoluchowski dynamics.

Contribution

It introduces a novel field theoretic approach to kinetic theory, providing a systematic perturbation framework for analyzing dense fluid dynamics and transitions.

Findings

Established a perturbation theory for kinetic field variables

Derived cumulants in the noninteracting limit

Set up the foundation for analyzing ergodic-nonergodic transitions

Abstract

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables \rho the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables \rho and B.