Kinetic Field Theory: Higher-Order Perturbation Theory

TL;DR

This paper presents a detailed formalism of Kinetic Field Theory (KFT) for non-equilibrium classical systems, emphasizing a perturbative approach that improves interpretability and applies to cosmic structure formation.

Contribution

It introduces a refined perturbative method in KFT by delaying integration over initial conditions, enhancing clarity and physical insight, especially for cosmic structure modeling.

Findings

Reproduces linear growth of cosmic density fluctuations from particle dynamics.

Improves perturbative calculations by integrating over initial conditions last.

Provides a comprehensive framework for non-equilibrium classical field systems.

Abstract

We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation of classical mechanics, employing the powerful techniques developed in the context of quantum field theory to describe classical systems. Unlike previous work on KFT, we perform the integration over the probability distribution of initial conditions in the very last step. This significantly improves the clarity of the perturbative treatment and allows for physical interpretation of intermediate results. We give an introduction to the general framework, but focus on the application to interacting $N$-body systems. Specializing the results to cosmic structure formation, we reproduce the linear growth of the cosmic density fluctuation power spectrum on all scales from microscopic, Newtonian particle dynamics alone.