Fedosov quantization of Lagrange-Finsler and Hamilton-Cartan spaces and Einstein gravity lifts on (co) tangent bundles

Journal of Mathematical Physics

Volumn 50, Issue 1, 2009, Pages

  Anastasiei, M ^a,b   Vacaru, Sergiu I ^a,c  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

^b ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^c FIELDS INSTITUTE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59349101225     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3043786     Document Type: Article

References (56)

1. I. Batalin, E. Fradkin, and T. Fradkina, Nucl. Phys. B 332, 224 (1990).
2. B. de Wit and J. W. van Holten, Phys. Lett. 79B, 389 (1978).
3. M. Grigoriev and S. Lyakhovich, Commun. Math. Phys. 218, 437 (2001).
4. M. Henneaux, Phys. Rep. 126, 1 (1985).
5. B. Fedosov, J. Diff. Geom. 40, 213 (1994).
6. B. Fedosov, Deformation Quantization and Index Theory, Mathematical Topics Vol. 9 (Akademie-Verlag, Berlin, 1996).
7. M. Kontsevich, Lett. Math. Phys. 66, 157 (2003).
8. M. Kontsevich, Lett. Math. Phys. 48, 35 (1999).
9. P. Kazinski, S. Lyakhovich, and A. Sharapov, J. High Energy Phys. 0507, 076 (2005).
10. S. Lyakhovich and A. Sharapov, J. High Energy Phys. 0503, 011 (2005).
11. C. Castro, J. Geom. Phys. 33, 173 (2000).
12. C. Castro, Gen. Relativ. Gravit. 36, 2605 (2004).
13. C. Castro, Phys. Lett. B 668, 442 (2008).
14. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004).
15. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 21, R53 (2004).
16. T. Thiemann, Modern Canonical Quantum General Relativity (Cambrdigde University Press, Cambridge, 2006).
17. I. Gorbunov, S. Lyakhovich, and A. Sharapov, J. Geom. Phys. 53, 98 (2005).
18. I. Batalin, M. Grigoriev, and S. Lyakhovich, J. Math. Phys. 46, 072301 (2005).
19. A. Karabegov, Commun. Math. Phys. 258, 223 (2005).
20. F. Etayo, R. Santamaría, and S. Vacaru, J. Math. Phys. 46, 032901 (2005).
21. S. Vacaru, J. Math. Phys. 48, 123509 (2007).
22. S. Vacaru, e-print arXiv:0707.1526.
23. S. Vacaru, Phys. Lett. A 372, 2949 (2008).
24. S. Vacaru, e-print arXiv:0709.3609.
25. G. Vrnceanu, Acad. Sci., Paris, C. R. 103, 852 (1926).
26. G. Vrnceanu, Bull. Fac. St. Cernauti 5, 177 (1931).
27. G. Vrnceanu, Lȩons de Geometrie Differentielle (l'Academie de la Republique Populaire de Roumanie, Bucharest, 1957), Vol. II.
28. A. Bejancu and H. R. Farran, Foliations and Geometric Structures (Springer, New York, 2005).
29. S. Vacaru, P. Stavrinos, E. Gaburov, and D. Gona, Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity, Selected Works, Differential Geometry-Dynamical Systems, Monograph 7 (Geometry Balkan Press, Bucharest, 2006); www.mathem.pub.ro/dgds/mono-va-t.pdf; e-print arXiv:gr-qc0508023.
30. S. Vacaru, e-print arXiv:0707.1524.
31. R. Miron, D. Hrimiuc, H. Shimada, and V. S. Sabau, The Geometry of Hamilton and Lagrange Spaces (Kluwer Academic, Dordrecht, 2000).
32. R. Miron, The Geometry of Higher-Order Hamilton Spaces (Kluwer Academic, Dordrecht, 2003).
33. R. Miron and M. Anastasiei, Vector Bundles and Lagrange Spaces with Applications to Relativity (Geometry Balkan Press, Bucharest, 1997) [translation from Romanian of Editura Academiei Romane (1987)].
34. R. Miron and M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications (Kluwer Academic, Dordrecht, 1994).
35. A. Karabegov and M. Schlichenmaier, Lett. Math. Phys. 57, 135 (2001).
36. A. Karabegov, Lett. Math. Phys. 65, 133 (2003).
37. S. Vacaru and P. Stavrinos, Spinors and Space-Time Anisotropy (Athens University Press, Athens, 2002); e-print arXiv:gr-qc0112028.
38. S. Vacaru, J. Math. Phys. 37, 508 (1996).
39. S. Vacaru, J. High Energy Phys. 09, 011 (1998).
40. S. Vacaru, Ann. Phys. (N.Y.) 256, 39 (1997).
41. S. Vacaru, Nucl. Phys. B 434, 590 (1997).
42. N. Mavromatos, e-print arXiv:0708.2250.
43. F. Girelli, S. Liberati, and L. Sindoni, Phys. Rev. D 75, 064015 (2007).
44. S. Mignemi, Phys. Rev. D 76, 047702 (2007).
45. G. Gibbons, J. Gomis, and C. N. Pope, Phys. Rev. D 76, 081701 (2007).
46. R. Miron and Gh. Atanasiu, Kodai Math. J. 6, 228 (1983).
47. Gh. Atanasiu, M. Hashiguchi, and R. Miron, Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem. No. 18, 19 (1985).
48. S. Vacaru, e-print: arXiv:0806.3810.
49. S. Vacaru, Symmetry, Integr. Geom.: Methods Appl. 4, 071 (2008).
50. S. Vacaru, Int. J. Theor. Phys. (to be published).
51. C. Misner, K. Thorne, and J. Wheeler, Gravitation (Freeman, San Francisco, 1973).
52. M. Bordemann, N. Neumaier, and S. Waldman, Commun. Math. Phys. 198, 363 (1998).
53. M. Bordemann, N. Neumaier, and S. Waldman, J. Geom. Phys. 29, 199 (1999).
54. G. Barnich, M. Grigoriev, A. Semikhatov, and I. Tipunin, Commun. Math. Phys. 260, 147 (2005).
55. M. A. Vasiliev, Int. J. Geom. Methods Mod. Phys. 3, 37 (2006).
56. M. Grigoriev, e-print arXiv:hep-th0605089.