Supersymmetric hydrodynamics

Nyawelo, Tino S.

doi:10.1016/j.nuclphysb.2003.09.038

Cited by 11 publications

(15 citation statements)

References 10 publications

(21 reference statements)

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“…From the Fourier transform (22) and the definition of the ⋆-product (19) we can derive the first term of the Lagrangian L s [j µ (x), θ(x), α(x), β(x)] as follows…”

Section: Action Of the Noncommutative Fluidmentioning

confidence: 99%

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Noncommutative fluid dynamics in the Snyder space-time

et al. 2012

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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. *

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“…From the Fourier transform (22) and the definition of the ⋆-product (19) we can derive the first term of the Lagrangian L s [j µ (x), θ(x), α(x), β(x)] as follows…”

Section: Action Of the Noncommutative Fluidmentioning

confidence: 99%

“…As shown in [16], the description of the fluid degrees of freedom in terms of fluid potentials allows one to lift the obstruction to inverting the symplectic form in the canonical phase space of the fluid variables. (For other applications of the Kähler parametrization of the fluid potentials see [18,20,21,22,23,24,25]. )…”

Section: Introductionmentioning

confidence: 99%

Noncommutative fluid dynamics in the Snyder space-time

et al. 2012

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“…Thus, by requiring that the Lagrangian be invariant under the volume preserving transformations constraints need to be imposed on these functions. It can be easily verified that the fields of the theory transform under (20) as follows…”

Section: Volume Preserving Symmetrymentioning

confidence: 99%

Noncommutative fluid dynamics in the Kähler parametrization

Holender¹,

Santos²,

Orlando³

et al. 2011

Phys. Rev. D

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In this paper, we propose a first order action functional for a large class of systems that generalize the relativistic perfect fluids in the Kähler parametrization to noncommutative spacetimes. The noncommutative action is parametrized by two arbitrary functions K(z,z) and f ( √ −j 2 ) that depend on the fluid potentials and represent the generalization of the Kähler potential of the complex surface parametrized by z andz, respectively, and the characteristic function of each model. We calculate the equations of motion for the fluid potentials and the energy-momentum tensor in the first order in the noncommutative parameter. The density current does not receive any noncommutative corrections and it is conserved under the action of the commutative generators P µ but the energy-momentum tensor is not. Therefore, we determine the set of constraints under which the energy-momentum tensor is divergenceless. Another set of constraints on the fluid potentials is obtained from the requirement of the invariance of the action under the generalization of the volume preserving transformations of the noncommutative spacetime. We show that the proposed action describes noncommutative fluid models by casting the energy-momentum tensor in the familiar fluid form and identifying the corresponding energy and momentum densities. In the commutative limit, they are identical to the corresponding quantities of the relativistic perfect fluids. The energy-momentum tensor contains a dissipative term that is due to the noncommutative spacetime and vanishes in the commutative limit. Finally, we particularize the theory to the case when the complex fluid potentials are characterized by a function K(z,z) that is a deformation of the complex plane and show that this model has important common features with the commutative fluid such as infinitely many conserved currents and a conserved axial current that in the commutative case is associated to the topologically conserved linking number. *

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“…The choice of the commutative fluid potentials is not unique. When it is made in terms of real functions θ(x), α(x) and β(x) it is called the Clebsch parametrization [35,36] while the fluid potentials given in terms of one real θ(x) and two complex functions z(x) andz(x), respectively, define the so called Kähler parametrization [37,38,39,40,41,42,43,44].…”

Section: Introductionmentioning

confidence: 99%

Plane waves in noncommutative fluids

et al. 2013

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We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monocromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated. *

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Supersymmetric hydrodynamics

Cited by 11 publications

References 10 publications

Noncommutative fluid dynamics in the Snyder space-time

Noncommutative fluid dynamics in the Snyder space-time

Noncommutative fluid dynamics in the Kähler parametrization

Plane waves in noncommutative fluids

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