Degenerate dynamical systems

Journal of Mathematical Physics

Volumn 42, Issue 9, 2001, Pages 4383-4390

  Saavedra, Joel ^a,b   Troncoso, Ricardo ^b   Zanelli, Jorge ^b  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^b CENTRO DE ESTUDIOS CIENTÍFICOS CECS   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035537188     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1389088     Document Type: Article

References (23)

1. See, e.g., H. Aref, Annu. Rev. Fluid Mech. 15, 345 (1983), and references therein.
2. C. Teitelboim and J. Zanelli, Class. Quantum Grav. 4, L125 (1987).
3. N. Deruelle and T. Dolezel, Phys. Rev. D 62, 103502 (2000).
4. S. W. Hawking, T. Hertog, and H. S. Reall, Phys. Rev. D 62, 043501 (2000).
5. P. Candelas, G. T. Horowitz, A. Strominger, and E. Witten, Nucl. Phys. B 258, 46 (1985).
6. M. Green and P. Vanhove, Phys. Lett. B 408, 122 (1997).
7. R. Troncoso and J. Zanelli, Phys. Rev. D 58, 101703(R) (1998).
8. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978); J. Math. Phys. 41, 3307 (2000); J. Cariñena, C. López, and M. Rañada, ibid., 29, 1134 (1988).
9. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978); J. Math. Phys. 41, 3307 (2000); J. Cariñena, C. López, and M. Rañada, ibid., 29, 1134 (1988).
10. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978); J. Math. Phys. 41, 3307 (2000); J. Cariñena, C. López, and M. Rañada, ibid., 29, 1134 (1988).
11. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton U. P., Princeton, NJ, 1993).
12. S. Hojman and L. F. Urrutia, J. Math. Phys. 22, 1896 (1981). The usefulness of this first order form has been emphasized in a different context in L. D. Faddeev and R. Jackiw, Phys. Rev. Lett. 60, 1692 (1988).
13. S. Hojman and L. F. Urrutia, J. Math. Phys. 22, 1896 (1981). The usefulness of this first order form has been emphasized in a different context in L. D. Faddeev and R. Jackiw, Phys. Rev. Lett. 60, 1692 (1988).
14. The subgroup of diffeomorphisms which can be realized in phase space are those which leave invariant the symplectic form. For a discussion on this see R. Floreanini, R. Percacci, and E. Sezgin, Nucl. Phys. B 322, 255 (1989).
15. The standard notion of symplectic form is usually assigned only to nonsingular closed two-forms. However, we extend the term "symplectic form" to the cases (B) and (C) later in this work.
16. ij) is less than maximal in the complement of Σ is a combination of cases (B) and (C). It is straighforward to consider this additional complication, but it does not add much to deserve an extensive discussion here.
17. The special case when there is a dense set of Poincaré singularities lying on Σ is excluded by our hypotheses. In that case the system can show a different behavior, which will be discussed elsewhere.
18. P. A. M. Dirac, Can. J. Math. 2, 147 (1950); Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University (Academic, New York, 1964).
19. P. A. M. Dirac, Can. J. Math. 2, 147 (1950); Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University (Academic, New York, 1964).
20. D. V. Choodnovsky and G. V. Choodnovsky, Nuovo Cimento Soc. Ital. Fis., B 40, 339 (1977).
21. A. Gomberoff, J. Saavedra, R. Troncoso, and J. Zanelli, work in progress.
22. M. Asorey, private communication.
23. N. Seiberg and E. Witten, J. High Energy Phys. 032, 9909 (1999).