The generalized Moyal-Nahm and continuous Moyal-Toda equations

Journal of Mathematical Physics

Volumn 40, Issue 8, 1999, Pages 3738-3760

  Castro, Carlos ^a,b   Plebański, Jerzy ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033241151     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532924     Document Type: Article

References (53)

1. ∞ String Sector of the Membrane," hep-th/9612160.
2. ∞ String Sector of the Membrane," hep-th/9612160.
3. ∞ String Sector of the Membrane," hep-th/9612160.
4. J. Hoppe, "Quantum Theory of a Relativistic Surface," Ph.D thesis, M.I.T. (1982).
5. E. Bergshoeff, E. Sezgin, Y. Tanni, and P. K. Townsend, Ann. Phys. 199, 340 (1990); B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B 305, 545 (1988) ; B. Biran, E. G. Floratos, and G. K. Saviddy, Phys. Lett. B 198, 32 (1987); T. Banks, W. Fischler, S. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).
6. E. Bergshoeff, E. Sezgin, Y. Tanni, and P. K. Townsend, Ann. Phys. 199, 340 (1990); B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B 305, 545 (1988) ; B. Biran, E. G. Floratos, and G. K. Saviddy, Phys. Lett. B 198, 32 (1987); T. Banks, W. Fischler, S. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).
7. E. Bergshoeff, E. Sezgin, Y. Tanni, and P. K. Townsend, Ann. Phys. 199, 340 (1990); B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B 305, 545 (1988) ; B. Biran, E. G. Floratos, and G. K. Saviddy, Phys. Lett. B 198, 32 (1987); T. Banks, W. Fischler, S. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).
8. E. Bergshoeff, E. Sezgin, Y. Tanni, and P. K. Townsend, Ann. Phys. 199, 340 (1990); B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B 305, 545 (1988) ; B. Biran, E. G. Floratos, and G. K. Saviddy, Phys. Lett. B 198, 32 (1987); T. Banks, W. Fischler, S. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).
9. T. A. Ivanova and A. D. Popov, J. Math. Phys. 34, 674 (1993); Theor. Math. Phys. 94, 225 (1993); Lett. Math. Phys. 23, 29 (1991); JETP Lett. 54, 69 (1991).
10. T. A. Ivanova and A. D. Popov, J. Math. Phys. 34, 674 (1993); Theor. Math. Phys. 94, 225 (1993); Lett. Math. Phys. 23, 29 (1991); JETP Lett. 54, 69 (1991).
11. T. A. Ivanova and A. D. Popov, J. Math. Phys. 34, 674 (1993); Theor. Math. Phys. 94, 225 (1993); Lett. Math. Phys. 23, 29 (1991); JETP Lett. 54, 69 (1991).
12. T. A. Ivanova and A. D. Popov, J. Math. Phys. 34, 674 (1993); Theor. Math. Phys. 94, 225 (1993); Lett. Math. Phys. 23, 29 (1991); JETP Lett. 54, 69 (1991).
13. E. G. Floratos and G. K. Leontaris, Phys. Lett. B 223, 153 (1989).
14. G. Chapline and K. Yamagishi, Class. Quantum Grav. 8, 427 (1991); Phys. Rev. Lett. 66, 3064 (1991); G. Chapline, Mod. Phys. Lett. A 7, 1959 (1992).
15. G. Chapline and K. Yamagishi, Class. Quantum Grav. 8, 427 (1991); Phys. Rev. Lett. 66, 3064 (1991); G. Chapline, Mod. Phys. Lett. A 7, 1959 (1992).
16. G. Chapline and K. Yamagishi, Class. Quantum Grav. 8, 427 (1991); Phys. Rev. Lett. 66, 3064 (1991); G. Chapline, Mod. Phys. Lett. A 7, 1959 (1992).
17. C. D. Boyer and J. Finley III, J. Math. Phys. 23, 1126 (1982); Q. H. Park, Int. J. Mod. Phys. A 7, 1415 (1991).
18. C. D. Boyer and J. Finley III, J. Math. Phys. 23, 1126 (1982); Q. H. Park, Int. J. Mod. Phys. A 7, 1415 (1991).
19. C. Castro, J. Math. Phys. 34, 681 (1993); 35, 3013 (1994).
20. C. Castro, J. Math. Phys. 34, 681 (1993); 35, 3013 (1994).
21. J. Plebański and M. Przanowski, Phys. Lett. A 219, 249 (1996).
22. C. Castro, Phys. Lett. B 413, 53 (1997).
23. H. Garcia-Compeán and J. Plebański, Phys. Lett. A 234, 5 (1997).
24. H. Weyl, Z. Phys. 46, 1 (1927); E. Wigner, Phys. Rev. 40, 749 (1932); J. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1945); H. J Groenwold, Physica (Amsterdam) 12, 405 (1946).
25. H. Weyl, Z. Phys. 46, 1 (1927); E. Wigner, Phys. Rev. 40, 749 (1932); J. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1945); H. J Groenwold, Physica (Amsterdam) 12, 405 (1946).
26. H. Weyl, Z. Phys. 46, 1 (1927); E. Wigner, Phys. Rev. 40, 749 (1932); J. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1945); H. J Groenwold, Physica (Amsterdam) 12, 405 (1946).
27. H. Weyl, Z. Phys. 46, 1 (1927); E. Wigner, Phys. Rev. 40, 749 (1932); J. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1945); H. J Groenwold, Physica (Amsterdam) 12, 405 (1946).
28. D. Fairlie, C. Zachos, and T. Curtright, ́Matrix Membranes and Integrability,́ hep-th/9709042.
29. D. Fairlie, C. Zachos, and T. Curtright, ́Matrix Membranes and Integrability,́ hep-th/9709042.
30. I. A. B. Strachan, Phys. Lett. B 282, 63 (1992); J. Geom. Phys. 21, 255 (1997); J. Phys. A 29, 6117 (1996); private communication.
31. I. A. B. Strachan, Phys. Lett. B 282, 63 (1992); J. Geom. Phys. 21, 255 (1997); J. Phys. A 29, 6117 (1996); private communication.
32. I. A. B. Strachan, Phys. Lett. B 282, 63 (1992); J. Geom. Phys. 21, 255 (1997); J. Phys. A 29, 6117 (1996); private communication.
33. K. Takasaki and P. Guha, "Dispersionless Hierarchies, Hamilton Iacobi Theory and Twistor Correspondences," solv-int/9705013.
34. G. Dito, M. Flato, D. Sternheimer, and L. Takhtajan, "Deformation Quantization and Nambu Mechanics," hep-th/9602016.
35. C. Castro, in preparation.
36. M. Przanowski and S. Formański, "Searching for a universal integrable system," University of Lodz preprint, May 1997, to be published in Acta Phys. Pol. B.
37. M. Saveliev, Theor. Math. Phys. 92, 457 (1992); M. Saveliev and A. Vershik, Phys. Lett. A 143, 121 (1990).
38. M. Saveliev, Theor. Math. Phys. 92, 457 (1992); M. Saveliev and A. Vershik, Phys. Lett. A 143, 121 (1990).
39. I. Bakas and E. Kiritsis, in "Common Trends in Mathematics and Quantum Field Theories," edited by T. Eguchi, T. Inami, and T. Miwa (Prog. Theor. Phys. Supplement, 1990).
40. G. W Gibbons and S. W Hawking, Phys. Lett. B 78, 430 (1978); T. Eguchi and A. J. Hanson, Phys. Lett. B 74, 249 (1978).
41. G. W Gibbons and S. W Hawking, Phys. Lett. B 78, 430 (1978); T. Eguchi and A. J. Hanson, Phys. Lett. B 74, 249 (1978).
42. M. K Prasad, Phys. Lett. B 83, 310 (1979).
43. B. Fedosov, J. Diff. Geom. 40, 213 (1994); M. Reuter, "Non-Commutative Geometry of Quantum Phase Space," hep-th/9510011; H. Garcia-Compean, J. Plebański, and M. Przanowski, Acta Phys. Pol. B 29, 549 (1998).
44. B. Fedosov, J. Diff. Geom. 40, 213 (1994); M. Reuter, "Non-Commutative Geometry of Quantum Phase Space," hep-th/9510011; H. Garcia-Compean, J. Plebański, and M. Przanowski, Acta Phys. Pol. B 29, 549 (1998).
45. B. Fedosov, J. Diff. Geom. 40, 213 (1994); M. Reuter, "Non-Commutative Geometry of Quantum Phase Space," hep-th/9510011; H. Garcia-Compean, J. Plebański, and M. Przanowski, Acta Phys. Pol. B 29, 549 (1998).
46. A. Dimakis and F. Muller-Hoissen, "Integrable discretizations of chiral models via deformation of the differential calculus," hep-th/9512007; "Deformations of classical geometries and integrable systems," physics/9712002.
47. A. Dimakis and F. Muller-Hoissen, "Integrable discretizations of chiral models via deformation of the differential calculus," hep-th/9512007; "Deformations of classical geometries and integrable systems," physics/9712002.
48. C. Castro, Phys. Lett. B 353, 201 (1995).
49. D. B. Fairlie and J. Nuyts, Commun. Math. Phys. 134, 413 (1990).
50. I. Bakas, B. Khesin, and E. Kiritsis, Commun. Math. Phys. 151, 233 (1993).
51. C. Pope, L. Romans, and X. Shen, Phys. Lett. B 236, 173 (1990).
52. D. Fairlie and T. Ueno, "Higher dimensional generalizations of the Euler Top Equations," hep-th/9710079; "General solution of the 7D octonionic top equations," hep-th/9801079.
53. D. Fairlie and T. Ueno, "Higher dimensional generalizations of the Euler Top Equations," hep-th/9710079; "General solution of the 7D octonionic top equations," hep-th/9801079.