Research

 

SL(2,R)-geometric phase space and (2+2)-dimensions

 

R. Flores^a, J. A. Nieto^b,a, J. Tellez^a, E. A. Leon^b, and E. R. Estrada^c

 

^a Departamento de Investigación en Física de la Universidad de Sonora, 83000, Hermosillo Sonora, México. e-mail: rflorese@gauss.mat.uson.mx; jtellez@cajeme.cifus.uson.mx.

^b Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán Sinaloa, México. e-mail: niet@uas.edu.mx; janieto1@asu.edu; ealeon@uas.edu.mx.

^c Instituto Tecnológico Superior de Eldorado, Eldorado, Sinaloa, México. e-mail: profe.emmanuel@gmail.com.

 

Received 23 November 2012
Accepted 19 April 2013

 

Abstract

We propose an alternative geometric mathematical structure for arbitrary phase space. The main guide in our approach is the hidden SL(2,R)-symmetry which acts on the phase space changing coordinates by momenta and vice versa. We show that the SL(2,R)-symmetry is implicit in any symplectic structure. We also prove that in any sensible physical theory based on the SL(2,R)-symmetry the signature of the flat target "spacetime" must be associated with either one-time and one-space or at least two-time and two-space coordinates. We discuss the consequences as well as possible applications of our approach on different physical scenarios.

Keywords: Symplectic geometry; constrained Hamiltonian systems; two time physics.

 

PACS: 04.20.Gz; 04.60.-Ds; 11.30.Ly

DESCARGAR ARTÍCULO EN FORMATO PDF 

 

Acknowledgments

This work was partially supported by PROFAPI-UAS 2009.

 

 

References

1. J.M. Maldacena and H. Ooguri, J. Math. Phys. 42 (2001) 2929; hep-th/0001053.         [ Links ]

2. E. Witten, Phys. Rev. D44 (1991) 314.         [ Links ]

3. O.F. Hernández, "An Understanding of SU(1,1) / U(1) conformal field theory via bosonization" , Presented at 4th Mexican School of Particles and Fields, Dec 2-12, 1990, (Oaxtepec, Mexico. Published in Mexican School 1990), 429-436.         [ Links ]

4. S. Hwang, Nucl. Phys. B354 (1991) 100 .         [ Links ]

5. I. Bars, Class. Quant. Grav. 18 (2001) 3113 ; hep-th/0008164.         [ Links ]

6. I. Bars, C. Deliduman and O. Andreev, Phys. Rev. D 58 (1998) 066004; hep-th/9803188.         [ Links ]

7. I. Bars, Int. J. Mod. Phys. A 25 (2010) 5235; arXiv:1004.0688 [hep-th]         [ Links ].

8. J.A. Nieto, Nuovo Cim. B120 (2005) 135; hep-th/0410003.         [ Links ]

9. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, New Jersey, 1992).         [ Links ]

10. J. Govaerts, Hamiltonian Quantisation and Constrained Dynamics (Leuven University Press, Leuven, 1991).         [ Links ]

11 . A. Hanson, T. Regge and C. Teitelboim, Constrained Hamilto-nian Systems (Accademia Nazionale dei Lincei, Roma, 1976).         [ Links ]

12. V.M. Villanueva, J.A. Nieto, L. Ruiz and J. Silvas, J. Phys. A 38 (2005) 7183; hep-th/0503093.         [ Links ]

13. J.M. Romero and A. Zamora, Phys. Rev. D 70 (2004) 105006; hep-th/0408193.         [ Links ]

14. P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).         [ Links ]

15. S.V. Ketov, H. Nishino and S. J. Gates Jr., Nucl. Phys. B 393 (1993) 149; hep-th/9207042.         [ Links ]

16. J.A. Nieto and E.A. Leon, Braz. J. Phys. 40 (2010) 383; arXiv:0905.3543 [hep-th]         [ Links ].

17. H. Ooguri and C. Vafa, Nucl. Phys. B367 (1991) 83.         [ Links ]

18. H. Ooguri and C. Vafa, Nucl. Phys. B361 (1991) 469.         [ Links ]

19. E. Sezgin, Is there a stringydescription ofselfdual supergrav-ity in (2+2)-dimensions?, Published in "Trieste High energy physics and cosmology" (1995) 360-369; hep-th/9602099.         [ Links ]

20. Z. Khviengia, H. Lu, C.N. Pope, E. Sezgin, X.J. Wang and K.W. Xu, Nucl. Phys. B 444 (1995) 468; hep-th/9504121.         [ Links ]

21. S.V. Ketov, Class. Quantum Grav. 10 (1993) 1689; hep-th/9302091.         [ Links ]

22. M.A. De Andrade, O.M. Del Cima and L.P. Colatto, Phys. Lett. B370 (1996) 59; hep-th/9506146.         [ Links ]

23. M.F. Atiyah. and R.S. Ward, Commun. Math. Phys. 55 (1977) 117.         [ Links ]

24. P.G.O. Freund, Introduction to Supersymmetry (Cambridge University Press, Melbourne, 1986).         [ Links ]

25. S.V. Ketov, H. Nishino and S.J. Gates Jr., Phys. Lett. B 307 (1993) 323; hep-th/9203081.         [ Links ]

26. J.A. Nieto, Rev. Mex. Fis. 57 (2011) 400; arXiv:1003.4750 [hep-th]         [ Links ].

27. J. A. Nieto, Int. J. Geom. Meth. Mod. Phys. 09 (2012) 1250069; arXiv:1107.0718 [gr-qc]         [ Links ].

28. J.A. Nieto, Adv. Theor. Math. Phys. 10 (2006) 747; hep-th/0506106.         [ Links ]

29. J.A. Nieto, Adv. Theor. Math. Phys. 8 (2004) 177; hep-th/0310071.         [ Links ]

30. C.M. Hull, JHEP9811 (1998) 017; hep-th/9807127.         [ Links ]