A Model for Hydrodynamics in Kinetic Field Theory

TL;DR

This paper develops an effective kinetic field theory model for ideal and viscous fluid dynamics, applicable to cosmic structure formation and potentially other fields, by introducing mesoscopic particles and deriving macroscopic equations.

Contribution

It introduces a novel mesoscopic particle-based model within kinetic field theory that reproduces key hydrodynamic equations for both ideal and viscous fluids.

Findings

Model reproduces continuity, Euler, Navier-Stokes, and energy equations.

Applicable to cosmic structure formation and beyond.

Framework bridges microscopic particle interactions with macroscopic fluid behavior.

Abstract

In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitable interaction operators. We then show that the model indeed leads to the correct macroscopic evolution equations, namely the continuity, Euler, Navier-Stokes, and energy conservation equations of both ideal and viscous hydrodynamics.