Noncommutative Metafluid Dynamics

TL;DR

This paper develops a noncommutative metafluid dynamics framework, applying Dirac's quantization, revealing gauge covariant equations, and showing how noncommutativity introduces new terms into dissipative forces.

Contribution

It introduces a gauge covariant quantization of noncommutative metafluid dynamics and demonstrates the effects of noncommutativity on dissipative forces and phase space transformations.

Findings

Gauge covariant equations of motion derived

Noncommutativity introduces additional dissipative terms

Transformation on classical phase space reproduces noncommutative results

Abstract

In this paper we define a noncommutative (NC) Metafluid Dynamics \cite{Marmanis}. We applied the Dirac's quantization to the Metafluid Dynamics on NC spaces. First class constraints were found which are the same obtained in \cite{BJP}. The gauge covariant quantization of the non-linear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation \cite{Djemai} on the usual classical phase space (CPS) leads to the same results as of the $\star$-deformation with $\nu=0$. Besides, we will shown that an additional term is introduced into the dissipative force due the NC geometry. This is an interesting feature due to the NC nature induced into model.