Noncommutative fluid dynamics in the Snyder space-time

TL;DR

This paper develops a noncommutative fluid model within Snyder space-time, extending classical fluid dynamics to a quantum-deformed geometric setting with preserved symmetries.

Contribution

It introduces the first noncommutative fluid model with deformed Poincare invariance using realization formalism, specific to Snyder space.

Findings

Derived fluid equations of motion in Snyder space

Constructed conserved energy-momentum tensor for the noncommutative fluid

Extended classical fluid dynamics to noncommutative geometry

Abstract

In this paper, we construct for the first time the non-commutative fluid with the deformed Poincare invariance. To this end, the realization formalism of the noncommutative spaces is employed and the results are particularized to the Snyder space. The non-commutative fluid generalizes the fluid model in the action functional formulation to the noncommutative space. The fluid equations of motion and the conserved energy-momentum tensor are obtained.