Quantum fluids in the Kaehler parametrization

TL;DR

This paper explores the quantization of perfect relativistic fluids using Kähler parametrization, employing the BRST method to analyze physical states, evolution, and path integrals in a generalized fluid model.

Contribution

It introduces a BRST-based quantization approach for relativistic fluids in Kähler parametrization, extending the analysis to a broad class of fluid models.

Findings

Successful formulation of the quantum theory of fluids in this framework

Explicit determination of physical states and their evolution

Development of a path integral approach for these fluids

Abstract

In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the K\"{a}hler parametrization. This fluid model describes a large set of interesting systems such as the power law energy density fluids, Chaplygin gas, etc. In order to maintain the generality of the model, we apply the BRST method in the reduced phase space in which the fluid degrees of freedom are just the fluid potentials and the fluid current is classically resolved in terms of them. We determine the physical states in this setting, the time evolution and the path integral formulation.