Abstract
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing in anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation.
Highlights
The above disconnected ideas have naturally led to attempts to formulate a generalization of canonical perfect fluid theory in NC space(time) where the space(time) is endowed with a noncommutative structure
In the present paper we develop a generalized fluid dynamics, compatible with NC space, from first principles
In the first part we have provided a new framework to consider a generalization of a perfect fluid model in noncommutative space
Summary
The above disconnected ideas have naturally led to attempts to formulate a generalization of canonical perfect fluid theory in NC space(time) where the space(time) is endowed with a noncommutative structure. The other alternative that is especially suited for fluids is to start from the Lagrangian (discrete) fluid model, introduce the NC space effect and subsequently exploit the map that connects the Lagrangian framework to an Euler Hamiltonian (continuum) framework to induce NC effects in the fluid field theory. We have followed the latter approach, the primary reason being that NC generalization can be unambiguously done in the discrete variable setup
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