Plane waves in noncommutative fluids

Abdalla, M. C. B.; Holender, L.; Santos, M.A. Couto dos; Vancea, Ion V.

doi:10.1016/j.physleta.2013.03.008

Cited by 3 publications

(2 citation statements)

References 52 publications

(110 reference statements)

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“…In this letter we have analyzed the whole phase space and its Hopf algebroid structure. The idea is to construct quantum field theory and gravity in the Hopf algebroid setting generalizing the ideas presented by the group of Wess et al In [56,57] NC fluid was analyzed. Using the realization formalism for Snyder space, fluid equations of motion and their perturbative solutions were derived.…”

Section: Exterior Derivative Nc Forms and κ-Deformed Super Algebramentioning

confidence: 99%

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

2013

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We unify κ-Poincaré algebra and κ-Minkowski spacetime by embedding them into quantum phase space.The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get κ-deformed Hopf algebroid structure and κ-deformed Heisenberg algebra. We explicitly construct κ-Poincaré-Hopf algebra and κ-Minkowski spacetime from twist. It is outlined how this construction can be extended to κ-deformed super algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.

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Section: Exterior Derivative Nc Forms and κ-Deformed Super Algebramentioning

confidence: 99%

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

2013

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“…Fluid equations of motion and their perturbative solutions were derived [98]. It is of interest to further investigate this line of research using realization formalism for more general NC spaces.…”

Section: Outlook and Discussionmentioning

confidence: 99%

Twists, realizations and Hopf algebroid structure of κ-deformed phase space

Jurić

Meljanac

Štrajn

2014

Int. J. Mod. Phys. A

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The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The κ-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many such realizations related by similarity transformations. For a given realization, we construct corresponding coproducts of commutative coordinates and momenta (bialgebroid structure). The κ-deformed phase space has twisted Hopf algebroid structure. General method for the construction of twist operator (satisfying cocycle and normalization condition) corresponding to deformed coalgebra structure is presented. Specially, twist for natural realization (classical basis) of κ-Minkowski space-time is presented. The cocycle condition, κ-Poincaré algebra and R-matrix are discussed. Twist operators in arbitrary realizations are constructed from the twist in the given realization using similarity transformations. Some examples are presented. The important physical applications of twists, realizations, R-matrix and Hopf algebroid structure are discussed. Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-3 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-4 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-5 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-6 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. multiplication map defined by m ⋆1 . The property of right ideal J is m ⋆ (J ⊲ (f ⊗ g)) = 0. For the right ideals J 0 and J , we have J 0 (H ⊗ H) = J 0 , J (H ⊗ H) = J , J = F J 0 F −1 = F J 0 , J J 0 ⊂ J , J 0 J ⊂ J 0 .

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

Saitou

Bamba

Sugamoto

2014

Progress of Theoretical and Experimental Physics

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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 θ, 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 θ. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined.

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Plane waves in noncommutative fluids

Cited by 3 publications

References 52 publications

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

Twists, realizations and Hopf algebroid structure of κ-deformed phase space

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

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