Noncommutative fluid dynamics in the Snyder space-time

Abstract

In this paper, we construct for the first time the noncommutative fluid with the deformed Poincaré invariance. To this end, the realization formalism of the noncommutative spaces is employed and the results are particularized to the Snyder space. The noncommutative 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. *

Noncommutative geometry and fluid dynamics

“…NC fluid dynamics, compatible with a Snyder form [21][22][23] of operatorial spacetime has been discussed in [15,16]. However, for the type of applications we have in mind, the simplest NC extension studied here induces very interesting and nontrivial effects in the fluid model and so other alternatives have not been considered, although these can be studied in our approach.…”

“…A form of "exotic plasma" fluid where the particle Lagrangian coordinates are endowed with an "exotic" algebra (that is, effectively a NC system), was studied in [54]. In another approach [15,16] NC effects, (of the same canonical form used here), were incorporated directly in the form of star products in the fluid action in Kahler parametrization to NC spacetimes. For completeness we show a few steps explicitly.…”

“…Incidentally we have put the 'time' in parentheses simply to indicate that conventionally the NC extension is restricted to the spatial sector only without affecting the time. Some relevant work in this context is [15][16][17].…”

“…See e.g. earlier reviews [18][19][20] for generic NC field theory construction and * -product formalism in [15,16] for NC fluid model. 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.…”

Plane waves in noncommutative fluids

“…Motivated by recent works in which several noncommutative systems of charges were shown to display fluid properties at quantum scale [1,2,3,4,5,6,7] as well as cosmological scale [8], we have proposed the first field theoretical model of fluid in the canonical noncommutative space [9] and the noncommutative Lorentz covariant space [10], respectively [11,12,45]. The noncommutative fluid was constructed as a noncommutative field theory [13,14] in the realization method approach [15,16,17,18,19,20,21,22,23,24,25,26,27] by generalizing the first order action functional of the commutative perfect relativistic fluid [28,29,30,31].…”