Twisted covariant noncommutative self-dual gravity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 78, Issue 12, 2008, Pages

  Estrada Jimenez S ^a   Garcia Compean H ^b   Obregon O ^c   Ramirez C ^d  

^a UNIVERSIDAD AUTÓNOMA DE CHIAPAS   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

^c UNIVERSITY OF GUANAJUATO   (Mexico)

^d BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58049113238     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.78.124008     Document Type: Article

References (74)

1. W. Heisenberg (private communication) to R. Peierls;
2. W. Pauli, Scientific Correspondence, edited by, Karl von Meyenn, (Springer-Verlag, Berlin, 1985), Vol. II, p. 15.
3. J. Wess, in Supersymmetry and unification of fundamental interactions: Proceedings, edited by, P. Nath, and, P.M. Zerwas, (DESY, Hamburg, 2002).
4. H.S. Snyder, Phys. Rev. 71, 38 (1947). PHRVAO 0031-899X 10.1103/PhysRev.71.38
5. H.S. Snyder, Phys. Rev. 72, 68 (1947). PHRVAO 0031-899X 10.1103/PhysRev.72.68
6. W. Bietenholz, arXiv:0806.3713.
7. H. Weyl, Group Theory and Quantum Mechanics (Dover, New York, 1931);
8. E.P. Wigner, Phys. Rev. 40, 749 (1932); PHRVAO 0031-899X 10.1103/PhysRev.40.749
9. A. Groenewold, Physica (Amsterdam) PHYSAG 0031-8914 12, 405 (1946); 10.1016/S0031-8914(46)80059-4
10. J.E. Moyal, Proc. Cambridge Philos. Soc. PCPSA4 0008-1981 45, 99 (1949). 10.1017/S0305004100000487
11. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys. (N.Y.) APNYA6 0003-4916 111, 61 (1978); 10.1016/0003-4916(78)90224-5
12. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys. (N.Y.) APNYA6 0003-4916 111, 111 (1978). 10.1016/0003-4916(78)90225-7
13. G. Dito and D. Sternheimer, arXiv:math/0201168;
14. C.K. Zachos, Int. J. Mod. Phys. A 17, 297 (2002). IMPAEF 0217-751X 10.1142/S0217751X02006079
15. A. Connes, Noncommutative Geometry (Academic Press, New York, 1994).
16. J. von Neumann, Math. Ann. 104, 570 (1931). MAANA3 0025-5831 10.1007/BF01457956
17. I.M. Gelfand and M.A. Naimark, Mat. Sbornik MATSAB 0368-8666 12, 197 (1943).
18. N. Seiberg and E. Witten, J. High Energy Phys. JHEPFG 1029-8479 09 (1999) 032. 10.1088/1126-6708/1999/09/032
19. A. Connes, M.R. Douglas, and A. Schwarz, J. High Energy Phys. JHEPFG 1029-8479 02 (1998) 003. 10.1088/1126-6708/1998/02/003
20. S. Minwalla, M. Van Raamsdonk and N. Seiberg, J. High Energy Phys. JHEPFG 1029-8479 02 (2000) 020. 10.1088/1126-6708/2000/02/020
21. M.R. Douglas and N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001); RMPHAT 0034-6861 10.1103/RevModPhys.73.977
22. R.J. Szabo, Phys. Rep. PRPLCM 0370-1573 378, 207 (2003). 10.1016/S0370-1573(03)00059-0
23. J.M. Gracia-Bondia, J.C. Varilly, and H. Figueroa, Elements of Noncommutative Geometry (Birkhaeuser, Boston, 2001), p. 685.
24. M. Panero, J. High Energy Phys. JHEPFG 1029-8479 05 (2007) 082; 10.1088/1126-6708/2007/05/082
25. M. Panero SIGMA 1815-0659 2, 081 (2006).
26. M. Hayakawa, Phys. Lett. B 478, 394 (2000); PYLBAJ 0370-2693 10.1016/S0370-2693(00)00242-2
27. J. Madore, S. Schraml, P. Schupp, and J. Wess, Eur. Phys. J. C 16, 161 (2000); EPCFFB 1434-6044 10.1007/s100520050012
28. B. Jurco, S. Schraml, P. Schupp, and J. Wess, Eur. Phys. J. C 17, 521 (2000); EPCFFB 1434-6044 10.1007/s100520000487
29. X. Calmet, B. Jurco, P. Schupp, J. Wess, and M. Wohlgenannt, Eur. Phys. J. C 23, 363 (2002); EPCFFB 1434-6044 10.1007/s100520100873
30. P. Aschieri, B. Jurco, P. Schupp, and J. Wess, Nucl. Phys. NUPBBO 0550-3213 B651, 45 (2003). 10.1016/S0550-3213(02)00937-9
31. H. García-Compeán, O. Obregón, C. Ramírez, and M. Sabido, Phys. Rev. D PRVDAQ 0556-2821 68, 045010 (2003); 10.1103/PhysRevD.68.045010
32. H. García-Compeán O. Obregón C. Ramírez M. Sabido Phys. Rev. D PRVDAQ 0556-2821 68, 044015 (2003). 10.1103/PhysRevD.68. 044015
33. A.H. Chamseddine, G. Felder, J. Frohlich, Commun. Math. Phys. 155, 205 (1993); CMPHAY 0010-3616 10.1007/BF02100059
34. J. Madore, J. Mourad, Int. J. Mod. Phys. D 3, 221 (1994); IMPDEO 0218-2718 10.1142/S0218271894000332
35. A. Jevicki, S. Ramgoolam, J. High Energy Phys. JHEPFG 1029-8479 04 (1999) 032; 10.1088/1126-6708/1999/04/032
36. J.W. Moffat, Phys. Lett. B 491, 345 (2000); PYLBAJ 0370-2693 10.1016/S0370-2693(00)01064-9
37. A.H. Chamseddine, Commun. Math. Phys. 218, 283 (2001); CMPHAY 0010-3616 10.1007/s002200100393
38. H. Nishino, S. Rajpoot, Phys. Lett. B 532, 334 (2002); PYLBAJ 0370-2693 10.1016/S0370-2693(02)01533-2
39. A.H. Chamseddine, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 44, 2534 (2003); 10.1063/1.1572199
40. M.A. Cardella, D. Zanon, Classical Quantum Gravity CQGRDG 0264-9381 20, L95 (2003); 10.1088/0264-9381/20/8/101
41. A.H. Chamseddine, Phys. Rev. D PRVDAQ 0556-2821 69, 024015 (2004); 10.1103/PhysRevD.69.024015
42. D.V. Vassilevich, Nucl. Phys. NUPBBO 0550-3213 B715, 695 (2005); 10.1016/j.nuclphysb.2005.02.003
43. A.H. Chamseddine, Annales Henri Poincare 1424-0637 4S2, S881 (2003); 10.1007/s00023-003-0968-0
44. S. Marculescu and F.R. Ruiz, Phys. Rev. D PRVDAQ 1550-7998 74, 105004 (2006); 10.1103/PhysRevD.74.105004
45. R. Banerjee, P. Mukherjee, and S. Samanta, Phys. Rev. D PRVDAQ 1550-7998 75, 125020 (2007); 10.1103/PhysRevD.75.125020
46. J.A. Nieto, arXiv:0809.3429.
47. L. Alvarez-Gaume, F. Meyer, and M.A. Vazquez-Mozo, Nucl. Phys. NUPBBO 0550-3213 B753, 92 (2006). 10.1016/j.nuclphysb.2006.07.009
48. N. Seiberg, L. Susskind, and N. Toumbas, J. High Energy Phys. JHEPFG 1029-8479 06 (2000) 044. 10.1088/1126-6708/2000/06/044
49. J. Wess, " Deformed Coordinate Spaces; Derivatives, " BW2003 Workshop 2003.
50. Chaichian, P. Kulish, K. Nishijima, and A. Tureanu, Phys. Lett. B PYLBAJ 0370-2693 604, 98 (2004). 10.1016/j.physletb.2004.10.045
51. F. Koch and E. Tsouchnika, Nucl. Phys. NUPBBO 0550-3213 B717, 387 (2005). 10.1016/j.nuclphysb.2005.04.019
52. R. Oeckl, Nucl. Phys. NUPBBO 0550-3213 B581, 559 (2000). 10.1016/S0550-3213(00)00281-9
53. M. Dimitrijevic and J. Wess, " Deformed Bialgebra of Diffeomorphisms, " 1st Vienna Central European Seminar on Particle Physics and Quantum Field Theory 2004.
54. P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Shupp, and J. Wess, Classical Quantum Gravity CQGRDG 0264-9381 22, 3511 (2005). 10.1088/0264-9381/22/17/011
55. P. Aschieri, M. Dimitrijevic, F. Meyer, and J. Wess, Classical Quantum Gravity CQGRDG 0264-9381 23, 1883 (2006). 10.1088/0264-9381/23/6/005
56. J. Wess, SIGMA 2, 089 (2006); 1815-0659
57. P. Aschieri, J. Phys. Conf. Ser. 53, 799 (2006); 1742-6588 10.1088/1742-6596/53/1/052
58. P. Aschieri, Fortschr. Phys. FPYKA6 0015-8208 55, 649 (2007); 10.1002/prop.200610389
59. R.J. Szabo, Classical Quantum Gravity CQGRDG 0264-9381 23, R199 (2006). 10.1088/0264-9381/23/22/R01
60. D.V. Vassilevich, Mod. Phys. Lett. A 21, 1279 (2006). MPLAEQ 0217-7323 10.1142/S0217732306020755
61. P. Aschieri, M. Dimitrijevic, F. Meyer, S. Schraml, and J. Wess, Lett. Math. Phys. 78, 61 (2006). LMPHDY 0377-9017 10.1007/s11005-006-0108-0
62. R. Banerjee and S. Samanta, Eur. Phys. J. C 51, 207 (2007); EPCFFB 1434-6044 10.1140/epjc/s10052-007-0280-0
63. R. Banerjee S. Samanta J. High Energy Phys. JHEPFG 1029-8479 02 (2007) 046; 10.1088/1126-6708/2007/02/046
64. A. Kobakhidze, Int. J. Mod. Phys. A 23, 2541 (2008); IMPAEF 0217-751X 10.1142/S0217751X08041190
65. A.P. Balachandran, A. Pinzul, B.A. Qureshi, S. Vaidya, and I.I.S. Bangalore, arXiv:hep-th/0608138;
66. Y. Lee, Phys. Rev. D PRVDAQ 1550-7998 76, 025022 (2007); 10.1103/PhysRevD.76.025022
67. A.P. Balachandran, A. Pinzul, B.A. Qureshi, and S. Vaidya, Phys. Rev. D PRVDAQ 1550-7998 76, 105025 (2007). 10.1103/PhysRevD.76.105025
68. J. Wess, J. Phys. Conf. Ser. 53, 752 (2006). 1742-6588 10.1088/1742-6596/53/1/049
69. J. Plebański, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 18, 2511 (1977). 10.1063/1.523215
70. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986); PRLTAO 0031-9007 10.1103/PhysRevLett.57.2244
71. A. Ashtekar Phys. Rev. D PRVDAQ 0556-2821 36, 1587 (1987); 10.1103/PhysRevD.36.1587
72. A. Ashtekar Lectures on Non-perturbative Canonical Gravity (World Scientific, Singapore, 1991).
73. V. Chari and A.N. Pressley, A Guide to Quantum Groups (Cambridge University Press, Cambridge, England, 1995).
74. V.G. Drinfeld, Alg. Anal. 1, 114 (1989).