Quantum fluids in the Kähler parametrization

Abstract

In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the Kähler 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. *

Noncommutative fluid dynamics in the Snyder space-time

“…The relations (21), (24) and (25) lead to the following action of the noncommutative fluid defined on the algebra (C ∞ (M), ⋆)…”

“…As shown in [16], the description of the fluid degrees of freedom in terms of fluid potentials allows one to lift the obstruction to inverting the symplectic form in the canonical phase space of the fluid variables. (For other applications of the Kähler parametrization of the fluid potentials see [18,20,21,22,23,24,25]. )…”

Plane waves in noncommutative fluids

“…The choice of the commutative fluid potentials is not unique. When it is made in terms of real functions θ(x), α(x) and β(x) it is called the Clebsch parametrization [35,36] while the fluid potentials given in terms of one real θ(x) and two complex functions z(x) andz(x), respectively, define the so called Kähler parametrization [37,38,39,40,41,42,43,44].…”