Classical and quantum Nambu mechanics

Physical Review D

Volumn 68, Issue 8, 2003, Pages

  Curtright, Thomas ^a   Zachos, Cosmas ^b  

^a Department of Biology   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS; QUANTUM THEORY; STANDARD;

EID: 0344443289     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.085001     Document Type: Article

References (55)

1. Y. Nambu, Phys. Rev. D 7, 2405 (1973).
2. F. Bayen and M. Flato, Phys. Rev. D 11, 3049 (1975).
3. R. Chatterjee, Lett. Math. Phys. 36, 117 (1996).
4. N. Mukunda and E. Sudarshan, Phys. Rev. D 13, 2846 (1976).
5. P. Tempesta, A.V. Turbiner, and P. Winternitz, J. Math. Phys. 42, 4248 (2001).
6. T.L. Curtright and C.K. Zachos, New J. Phys. 4, 83 (2002); lectures delivered at the Workshop on Superintegrability in Classical and Quantum Systems, Centre de recherches mathématiques, Université de Montréal, 2002, math-ph/0211021;
7. in Short Distance Behavior of Fundamental Interactions, edited by Behram N. Kursunoglu, Metin Camcigil, Stephan L. Mintz, and Arnold Perlmutter, AIP Conf. Proc. No. 672 (AIP, Melville, NY, 2003), pp. 165-182, hep-th/0303088;
8. C. K. Zachos and T. L. Curtright, "Deformation Quantization, Superintegrability, and Nambu Mechanics," hep-th/0210170;
9. in Short Distance Behavior of Fundamental Interactions, ibid. pp. 183-196, quant-ph/0302106.
10. P. Gautheron. Lett. Math. Phys. 37, 103 (1996).
11. C. Gonera and Y. Nutku, Phys. Lett. A 285, 301 (2001).
12. D. Minic, "M Theory and Deformation Quantization," hep-th/9909022.
13. H. Awata, M. Li, D. Minic, and T. Yoneya, J. High Energy Phys. 02, 013 (2001).
14. J.A. de Azcárraga, J.M. Izquierdo, and J.C. Pérez Bueno, J. Phys. A 30, L607 (1997);
15. Rev. R. Acad. Cien. Exactas Fis. Nat. Ser. A Mat. 95, 225 (2001).
16. L. Baker and D.B. Fairlie, Nucl. Phys. B596, 348 (2001).
17. T. Curtright and D. Fairlie, J. Math. Phys. 44, 2692 (2003).
18. G. Dito, M. Flato, D. Sternheimer, and L. Takhtajan, Commun. Math. Phys. 183, 1 (1997).
19. J. Hoppe, Helv. Phys. Acta 70, 302 (1997).
20. R. Kerner, "Ternary Algebraic Structures and their Applications in Physics," math-ph/0011023.
21. Y. Matsuo and Y. Shibusa, J. High Energy Phys. 02, 006 (2001).
22. D. Minic and C.-H. Tze, Phys. Lett. B 536, 305 (2002).
23. B. Pioline, Phys. Rev. D 66, 025010 (2002).
24. L. Vainerman and R. Kerner, J. Math. Phys. 37, 2553 (1996).
25. F.B. Estabrook, Phys. Rev. D 8, 2740 (1973).
26. D. Sahoo and M.C. Valsakumar, Phys. Rev. A 46, 4410 (1992);
27. Mod. Phys. Lett. A 9, 2727 (1994).
28. M. Sakakibara, Prog. Theor. Phys. 104, 1067 (2000).
29. G. Dito and M. Flato, Lett. Math. Phys. 39, 107 (1997).
30. Chuan-sheng Xiong, Phys. Lett. B 486, 228 (2000).
31. L. Takhtajan, Commun. Math. Phys. 160, 295 (1994).
32. T. Curtright, in Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification, Proceedings of the 28th Orbis Scientiae Conference, 1999, edited by B. Kursunoglu, S. Mintz, and A. Perlmutter (Kluwer, New York, 2000), pp. 121-131, quant-ph/0011101.
33. F. Calogero and J.-P. Françoise, J. Nonlinear Math. Phys. 9, 99 (2002).
34. F. Calogero and J.-P. Françoise, lectures delivered at the Workshop on Superintegrability in Classical and Quantum Systems, Centre de recherches mathématiques, Université de Montréal, 2002.
35. N. Jacobson, Am. J. Math. 71, 149 (1949);
36. Trans. Am. Math. Soc. 70, 509 (1950).
37. P. Jordan, Z. Phys. 80, 285 (1933);
38. P. Jordan, J. von Neumann, and E. Wigner, Ann. Math. 35, 29 (1934).
39. A.J. Kalnay and R. Tascon, Phys. Rev. D 17, 1552 (1978).
40. W. Lister, Trends Genet. 72, 217 (1952).
41. M. Baranovich and M.S. Burgin, Russ. Math. Surveys 30, 65 (1975).
42. V.T. Filippov, Sib. Math. J. 26, 126 (1985);
43. V.T. Filippov, Sib. Math. J. 26, 879 (1986).
44. P. Higgins, Proc. London Math. Soc. 6, 366 (1956).
45. A.G. Kurosh, Russ. Math. Surveys 24, 1 (1969).
46. M. Schlesinger and J.D. Stasheff, J. Pure Appl. Algebra 38, 313 (1985).
47. P. Hanlon and M. Wachs, Adv. Math. 113, 206 (1995).
48. J. Hietarinta, J. Phys. A 30, L27 (1997).
49. J.A. de Azcárraga, A.M. Perelomov, and J.C. Pérez Bueno, J. Phys. A 29, 7993 (1996).
50. J.A. de Azcárraga and J.C. Pérez Bueno, Commun. Math. Phys. 184, 669 (1997).
51. A.C. Aitken, Determinants and Matrices (Greenwood, Weis Port, 1983).
52. Y. Nutku, J. Phys. A 36, 7559 (2003).
53. T. Curtright, T. Uematsu, and C. Zachos, Nucl. Phys. B469, 488 (1996).
54. E. Braaten, T. Curtright, and C. Zachos, Nucl. Phys. B260, 630 (1985).
55. S. Ayupov, A. Rakhimov, and S. Usmanov, Jordan, Real, and Lie Structures in Operator Algebras (Kluwer, Boston, 1997).