Noncommutativity from the symplectic point of view

International Journal of Modern Physics A

Volumn 21, Issue 26, 2006, Pages 5359-5369

  Abreu, E M C ^a   Neves, C ^b   Oliveira, W ^b  

^a FEDERAL RURAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b FEDERAL UNIVERSITY OF JUIZ DE FORA   (Brazil)

Author keywords

Noncommutativity; Symplectic formalism

Indexed keywords

EID: 33750920102     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X06034094     Document Type: Article

References (48)

1. A. Connes, M. Douglas and A. Schwarz, J. High Energy Phys. 02, 003 (1998).
2. N. A. Nekrasov, Trieste lectures on solitons in noncommutative gauge theories, hep-th/0011095.
3. A. Konechny and A. Schwarz, hep-th/0012145.
4. J. A. Harvey, Komada lectures on noncommutative solitons and D-branes, hep-th/0102076.
5. N. Seiberg and E. Witten, J. High Energy Phys. 09, 032 (1999).
6. R. Banerjee, Mod. Phys. Lett. A 17, 631 (2002).
7. G. 't Hooft, Class. Quantum Grav. 16. 3263 (1999).
8. G. 't Hooft, Determinism and dissipation in quantum gravity, hep-th/0003005.
9. G. 't Hooft, Quantum mechanics and determinism, hep-th/0105105.
10. A. A. Deriglazov, C. Neves and W. Oliveira, Open string with a background B-field as the first order mechanics and noncommutativity, hep-th/0110183.
11. N. Seiberg and E. Witten, J. High Energy Phys. 09, 032 (1999).
12. A. A. Deriglazov, Phys. Lett. B 530, 235 (2002).
13. A. A. Deriglazov, Phys. Lett. B 555, 83 (2003).
14. A. A. Deriglazov, Noncommutative version of an arbitrary nondegenerated mechanics, hep-th/0208072.
15. I. Y. Arefeva, D. M. Belov, A. A. Giryavets, A. S. Koshelev and P. B. Medvedev, Noncommutative field theories and (super) string field theories, hep-th/0111208.
16. R. J. Szabo, Quantum field theory on noncommutative spaces, hep-th/0109162.
17. O. F. Dayi and L. T. Kelleyane, Mod. Phys. Lett. A 17, 1937 (2002).
18. R. Amorim and J. Barcelos-Neto, Phys. Rev. D 64, 065013 (2001), and references therein.
19. P. A. Horváthy and M. S. Plyushchay, Phys. Lett. B 595, 547 (2004).
20. P. A. Horváthy and M. S. Plyushchay, J. High Energy Phys. 06, 033 (2002).
21. S. Minwalla, M. Van Raamsdonk and N. Seiberg, J. High Energy Phys. 02, 020 (2000).
22. A. E. F. Djemaï and H. Smail, Commun. Theor. Phys. 41, 837 (2004).
23. A. E. F. Djemaï and H. Smail, On noncommtative classical mechanics, hep-th/0309034.
24. A. E. F. Djemaï, Int. J. Theor. Phys. 35, 519 (1996).
25. P. A. M. Dirac, Proc. R. Soc. A 257, 32 (1960).
26. P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964).
27. A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian Systems (Academia Nazionale dei Lincei, Roma, 1976).
28. K. Sundermeyer, Constrained Dynamics, Lectures Notes in Physics, Vol. 169 (Springer, New York, 1982).
29. P. G. Bergmann, Phys. Rev. 75, 680 (1949).
30. P. G. Bergmann, Phys. Rev. 89, 4 (1953).
31. N. Banerjee, R. Banerjee and S. Ghosh, Ann. Phys. 241, 237 (1995), and references therein.
32. R. Rajaraman, Phys. Lett. B 154, 305 (1985).
33. J. Ananias Neto, C. Neves and W. Oliveira, Phys. Rev. D 63, 085018 (2001).
34. S.-T. Hong, Y.-W. Kim and Y.-J. Park, Mod. Phys. Lett. A 17, 435 (2002).
35. I. A. Batalin and E. S. Fradkin, Nucl. Phys. B 279, 514 (1987).
36. C. Wotzasek, Int. J. Mod. Phys. A 5, 1123 (1990).
37. C. Wotzasek, J. Math. Phys. 32, 540 (1991).
38. J. E. Moyal, Proc. Camb. Phil. Soc. 45, 99 (1949).
39. J. Vey, Commentarii Mathematici Helvetici 50, 421 (1975).
40. M. Flato et al., Commentarii Mathematici Helvetici 31, 47 (1975).
41. M. Flato et al., J. Math. Phys. 17, 1754 (1976).
42. F. Bayen et al., Ann. Phys. 111, 61 (1978).
43. P. A. Horváthy, Ann. Phys. 299, 128 (2002).
44. C. Neves and W. Oliveira, Phys. Lett. A 321, 267 (2004).
45. R. Floreanini and R. Jackiw, Phys. Rev. Lett. 59, 1873 (1987).
46. D. Bazeia, Mod. Phys. Lett. A 6, 1147 (1991).
47. R. Banerjee and S. Ghosh, J. Phys. A 31, L603 (1998).
48. R. Banerjee and P. Mukherjee, J. Phys. A 35, 5591 (2002).