"Gauging" the Fluid

TL;DR

This paper develops a Hamiltonian quantization framework for fluid models using gauge theory techniques, addressing non-canonical brackets and establishing equivalences with relativistic membranes.

Contribution

It introduces a gauge-invariant Hamiltonian quantization method for fluid models, overcoming non-canonical brackets and linking fluid dynamics with membrane theories.

Findings

Successful gauge-invariant quantization of fluid models.

Explicit relation between different gauge formulations.

Discussion of relativistic generalizations.

Abstract

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin \cite{12} quantization formalism is adopted in which the original system is converted to a local gauge theory and is embedded in a {\it canonical} extended phase space. In a different reduced phase space scheme \cite{vy} also the original model is converted to a gauge theory and subsequently the two distinct gauge invariant formulations of the fluid model are related explicitly. This strengthens the equivalence between the relativistic membrane (where a gauge invariance is manifest) and the fluid (where the gauge symmetry is hidden). Relativistic generalizations of the extended model is also touched upon.