Hamiltonian analysis of interacting fluids

TL;DR

This paper explores the Hamiltonian structure of ideal and interacting relativistic fluids, verifying fundamental conservation conditions, analyzing gauge interactions, and connecting relativistic and non-relativistic formulations.

Contribution

It provides a detailed Hamiltonian analysis of relativistic fluids, including interactions with gauge fields and a non-relativistic reduction, clarifying their stress tensor properties.

Findings

Verification of the Schwinger condition in different coordinate systems

Analysis of stress tensor conservation and its implications

Derivation of non-relativistic limits consistent with previous literature

Abstract

Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical(Noether) stress tensor and the symmetric one obtained by metric variation are discussed. Finally, a non-relativistic reduction of the system in light-cone coordinates has been carried out which reproduces results found earlier in the literature.