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We analyze the star product induced on the algebra of functions on R^3 by a suitable reduction of the Moyal product defined on F(R^4).
H. Weyl The theory of Groups and Quantum Mechanics Dover (1931), translation of Gruppentheorie und Quantemmechanik, Hirzel Verlag (1928)
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V. I. Manko, L. Rosa and P. Vitale, “Probability representation in quantum field theory,” Phys. Lett. B 439
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O. V. Man’ko, V. I. Man’ko and G. Marmo, “Star product of generalized Wigner-Weyl symbols on SU(2) group, deformations, and tomographic probability distribution,” Phys. Scripta 62
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J. M. Gracia-Bondía, F. Lizzi, G. Marmo and P. Vitale, “Infinitely many star products to play with,” JHEP 0204
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A. B. Hammou, M. Lagraa and M. M. Sheikh-Jabbari, “Coherent state induced star product on R**3(lambda) and the fuzzy sphere,” Phys. Rev. D 66
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L. Freidel and S. Majid, “Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity,” Class. Quant. Grav. 25
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E. Joung, J. Mourad and K. Noui, Three Dimensional Quantum Geometry and Deformed Poincare Symmetry,
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F. Lizzi, P. Vitale and A. Zampini, “The Fuzzy disc,” JHEP 0308
2003
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M. Kontsevich, “Deformation quantization of Poisson manifolds, I”, Lett. Math. Phys. 66 (2003) 157. [arXiv:q-alg/9709040]
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V. Gayral, J. M. Gracia-Bondia, B Iochum, T. Schücker and J. C. Varilly, Moyal planes are spectral triples, Comm. Math. Phys. 246 (2004) 569
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H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} theory on noncommutative ℝ 2 \mathbb{R}^{2} in the matrix base,” JHEP 0312 (2003) 019 H. Grosse and R. Wulkenhaar, “Renormalization of phi**4 theory on noncommutative R**4 in the matrix base,” Commun. Math. Phys. 256
2005
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G. Marmo, P. Vitale and A. Zampini “Noncommutative differential calculus for Moyal subalgebras” J. Geom. Phys. 56
2006
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V. I. Man’ko, G. Marmo and P. Vitale, “Duality symmetry for star products,” Phys. Lett. A 334 (2005) 1. [arXiv:hep-th/0407131]. O. V. Man’ko, V. I. Man’ko, G. Marmo and P. Vitale, “Star products, duality and double Lie algebras,” Phys. Lett. A 360 (2007) 522. [arXiv:quant-ph/0609041]
2007
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Patrizia Vitale, Jean-Christophe Wallet “Noncommutative field theories on ℝ λ 3 \mathbb{R}_{\lambda}^{3} and matrix models” Orsay preprint LPT-12-97
Cited in the paper.
2010
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Damien Calaque, Carlo A. Rossi ”Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry” (EMS Series of Lectures in Mathematics) (2011)
2011
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2011
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2011
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Patrizia Vitale ”Aspects of group field theory” AIP Conference Proceedings 1460
2012
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