Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--

TL;DR

This paper develops a new hydrodynamics framework on non-commutative space using Moyal brackets, aiming to model granular materials with a minimum volume, and explores its quantization and uncertainty relations.

Contribution

It introduces a non-commutative hydrodynamics model based on Nambu brackets replaced by Moyal brackets, linking to granular material behavior.

Findings

Derived a new hydrodynamics on non-commutative space.

Analyzed path integral quantization and uncertainty relations.

Proposed a connection to granular material physics.

Abstract

Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined.