Weyl-Wigner formulation of noncommutative quantum mechanics

Journal of Mathematical Physics

Volumn 49, Issue 7, 2008, Pages

  Bastos, Catarina ^a,c   Bertolami, Orfeu ^a,c   Dias, Nuno Costa ^b,d   Prata, João Nuno ^b,d  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSIDADE LUSÓFONA DE HUMANIDADES E TECNOLOGIAS   (Portugal)

^c Instituto de Plasmas e Fus o Nuclear

^d UNIVERSITY OF LISBON   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49249117893     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2944996     Document Type: Article

References (47)

1. P. -M. Ho and H. -C. Kao, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 88.151602 88, 151602 (2002).
2. V. P. Nair and A. P. Polychronakos, Phys. Lett. B 0370-2693 10.1016/S0370-2693(01)00339-2 505, 267 (2001).
3. C. Duval and P. A. Horvathy, J. Phys. A 0305-4470 10.1088/0305-4470/34/ 47/314 34, 10097 (2001).
4. P. A. Horvathy, Ann. Phys. (N.Y.) 0003-4916 10.1006/aphy.2002.6271 299, 128 (2002).
5. J. -Z. Zhang, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.93.043002 93, 043002 (2004).
6. J. -Z. Zhang, Phys. Lett. B 0370-2693 10.1016/j.physletb.2004.01.049 584, 204 (2004).
7. M. Demetrian and D. Kochan, Acta Phys. Slov. 52, 1 (2002).
8. J. Gamboa, M. Loewe, and J. C. Rojas, Phys. Rev. D 0556-2821 10.1103/PhysRevD.64.067901 64, 067901 (2001).
9. K. Li and S. Dulat, Eur. Phys. J. C 46, 825 (2006).
10. C. Acatrinei, Mod. Phys. Lett. A 0217-7323 10.1142/S0217732305017536 20, 1437 (2005).
11. O. Bertolami, J. G. Rosa, C. Aragão, P. Castorina, and D. Zappal̀, Phys. Rev. D 0556-2821 10.1103/PhysRevD.72.025010 72, 025010 (2005).
12. O. Bertolami, J. G. Rosa, C. Aragão, P. Castorina, and D. Zappal̀, Mod. Phys. Lett. A 0217-7323 10.1142/S0217732306019840 21, 795 (2006).
13. C. Bastos and O. Bertolami, e-print arXiv:gr-qc/0606131.
14. S. M. Carroll, J. A. Harvey, V. A. Kostelecký, C. D. Lane, and T. Okamoto, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.87.141601 87, 141601 (2001).
15. N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999).
16. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys. (N.Y.) 0003-4916 10.1016/0003-4916(78)90224-5 111, 61 (1978); F. Bayen, Ann. Phys. (N.Y.) 0003-4916 10.1016/0003-4916(78)90225-7 110, 111 (1978).
17. N. C. Dias and J. N. Prata, Ann. Phys. (N.Y.) 0003-4916 10.1016/j.aop.2003.11.004 311, 120 (2004).
18. N. C. Dias and J. N. Prata, Ann. Phys. (N.Y.) 0003-4916 10.1016/j.aop.2004.03.008 313, 110 (2004).
19. J. Vey, Comment. Math. Helv. 0010-2571 10.1007/BF02565761 50, 421 (1975).
20. N. C. Dias and J. N. Prata, J. Math. Phys. 0022-2488 10.1063/1.1415086 42, 5565 (2001).
21. N. C. Dias and J. N. Prata, J. Math. Phys. 0022-2488 10.1063/1.1641152 45, 887 (2004).
22. I. E. Segal, Math. Scand. 13, 31 (1963).
23. J. C. Pool, J. Math. Phys. 0022-2488 10.1063/1.1704817 7, 66 (1966).
24. D. Dubin, M. Hennings, and T. Smith, Mathematical Aspects of Weyl Quantization (World Scientific, Singapore, 2000).
25. M. Wilde and P. Lecomte, Lett. Math. Phys. 0377-9017 10.1007/BF00402248 7, 487 (1983).
26. M. Bordemann, N. Neumaier, and S. Waldmann, Commun. Math. Phys. 0010-3616 10.1007/s002200050481 198, 363 (1998).
27. B. Fedosov, J. Diff. Geom. 40, 213 (1994).
28. B. Fedosov, Deformation Quantization and Index Theory (Akademie, Berlin, 1996).
29. M. Kontsevich, Lett. Math. Phys. 0377-9017 10.1023/B:MATH.0000027508. 00421.bf 66, 157 (2003).
30. S. C. Jing, F. Zuo, and T. H. Heng, J. High Energy Phys. 0410, 049 (2004).
31. M. Rosenbaum, J. D. Vergara, and L. R. Juárez, Phys. Lett. A 354, 389 (2006). 0375-9601
32. B. Muthukumar, J. High Energy Phys. 0701, 073 (2007).
33. M. Rosenbaum and J. D. Vergara, Gen. Relativ. Gravit. 0001-7701 10.1007/s10714-006-0251-z 38, 607 (2006).
34. I. M. Gel'fand, G. E. Shilov, and N. Y. Vilenkin, Generalized Functions (Academic, New York, 1964), Vol. 1; Generalized Functions (Academic, New York, 1965), Vol. 2; Generalized Functions (Academic, New York, 1966), Vol. 3; Generalized Functions (Academic, New York, 1967), Vol. 4; Generalized Functions (Academic, New York, 1968), Vol. 5.
35. J. E. Roberts, J. Math. Phys. 0022-2488 10.1063/1.1705001 7, 1097 (1966).
36. J. P. Antoine, J. Math. Phys. 0022-2488 10.1063/1.1664761 10, 53 (1969); J. P. Antoine, J. Math. Phys. 10, 2276 (1969).
37. A. Bohm and M. Gadella, Dirac Kets, Gamow Vectors and Gel'fand Triplets: The Rigged Hilbert Space Formulation of Quantum Mechanics, Lectures in Mathematical Physics at the University of Texas at Austin (Springer-Verlag, Berlin, 1989).
38. L. Hörmander, The Analysis of Linear Partial Differential Operators I (Springer-Verlag, Berlin, 1983).
39. A. Zemanian, Distribution Theory and Transform Analysis (Dover, New York, 1987).
40. A. Bracken, G. Cassinelli, and J. Wood, e-print arXiv:math-ph/0211001.
41. H. Groenewold, Physica (Amsterdam) 0031-8914 10.1016/S0031-8914(46)80059- 4 12, 405 (1946).
42. J. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949). 0008-1981
43. G. Baker, Phys. Rev. 0031-899X 10.1103/PhysRev.109.2198 109, 2198 (1958).
44. E. Wigner, Phys. Rev. 0031-899X 10.1103/PhysRev.40.749 40, 749 (1932).
45. O. Bertolami and L. Guisado, Phys. Rev. D 0556-2821 10.1103/PhysRevD.67. 025001 67, 025001 (2003).
46. C. Bastos, O. Bertolami, N. C. Dias, and J. N. Prata (unpublished).
47. N. C. Dias and J. N. Prata, Ann. Phys. (N.Y.) (to appear).