Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Ballesteros, A. and Musso, F. , “Quantum algebras as quantizations of dual Poisson-Lie groups,” J. Phys. A: Math. Theor. 46, 195203 (2013).
Bastos, C. , Bertolami, O. , Dias, N. C. , and Prata, J. N. , “Weyl-Wigner formulation of noncommutative quantum mechanics,” J. Math. Phys. 49, 072101 (2008).
Bastos, C. , Dias, N. C. , and Prata, J. N. , “Wigner measures in noncommutative quantum mechanics,” Commun. Math. Phys. 299, 709 (2010).
Bonechi, F. , Giachetti, R. , Sorace, E. , and Tarlini, M. , “Deformation quantization of the heisenberg group,” Commun. Math. Phys. 169, 627 (1995).
Celeghini, E. , Giachetti, R. , Sorace, E. , and Tarlini, M. , “The quantum Heisenberg group H(1)q,” J. Math. Phys. 32, 1155 (1991).
Chari, V. and Pressley, A. N. , A Guide to Quantum Groups (Cambridge University Press, 1995).
Chowdhury, S. H. H. and Ali, S. T. , “The symmetry groups of noncommutative quantum mechanics and coherent state quantization,” J. Math. Phys. 54, 032101 (2013).
Chowdhury, S. H. H. and Ali, S. T. , “Triply extended group of translations of ℝ4 as defining group of NCQM: relation to various gauges,” J. Phys. A: Math. Theor. 47, 085301 (2014).
Chowdhury, S. H. H. and Ali, S. T. , “Wigner functions for noncommutative quantum mechanics: A group representation based construction,” J. Math. Phys. 56, 122102 (2015).
Dias, N. C. , de Gosson, M. , Luef, F. , and Prata, J. N. , “A deformation quantization theory for non-commutative quantum mechanics,” J. Math. Phys. 51, 072101 (2010).
Dias, N. C. , de Gosson, M. , Luef, F. , and Prata, J. N. , “A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces,” J. Math. Pures Appl. 96, 423445 (2011).
Doplicher, S. , Fredenhagen, K. , and Roberts, J. E. , “The quantum structure of spacetime at the Planck scale and quantum fields,” Commun. Math. Phys. 172, 187 (1995).
Hussin, V. , Lauzon, A. , and Rideau, G. , “R-matrix method for Heisenberg quantum groups,” Lett. Math. Phys. 39, 159 (1994).
Jing, S. , Zuo, F. , and Heng, T. , “Deformation quantization of noncommutative quantum mechanics,” J. High Energy Phys. 0410, 049 (2004).
Muthukumar, B. , “Remarks on the formulation of quantum mechanics on noncommutative phase spaces,” J. High Energy Phys. 0701, 073 (2007).
Rosenbaum, M. , Vergara, J. D. , and Juárez, L. R. , “Dynamical origin of the ⋆θ-noncommutativity in field theory from quantum mechanics,” Phys. Lett. A 354, 389395 (2006).
Snyder, H. S. , “Quantized space-time,” Phys. Rev. 71, 38 (1947).
Wigner, E. P. , “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749759 (1932).

Data & Media loading...


Article metrics loading...



In this paper, the Lie group , of which the kinematical symmetry group of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero , , and , is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. , 195203 (2013)]. A certain family of QUE algebras, corresponding to with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on .


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd