Investigación

 

Hamiltonian dynamics: four dimensional BF-like theories with a compact dimension

 

A. Escalante and M. Zarate Reyes

 

Instituto de Física Luis Rivera Terrazas, Benemérita Universidad Autónoma de Puebla, Apartado postal J-48 72570 Puebla. Pue., México, e-mail: aescalan@ifuap.buap.mx; mzarate@ifuap.buap.mx

 

Received 29 July 2015;
accepted 23 October 2015

 

Abstract

A detailed Dirac's canonical analysis for a topological four dimensional BF-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full structure of the constraints and the extended action. We show that the extended Hamiltonian is a linear combination of first class constraints, which means that the general covariance of the theory is not affected by the compactification process. Furthermore, in order to carry out the correct counting of physical degrees of freedom, we show that must be taken into account reducibility conditions among the first class constraints associated with the excited KK modes. Moreover, we perform the Hamiltonian analysis of Maxwell theory written as a BF-like theory with a compact dimension, we analyze the constraints of the theory and we calculate the fundamental Dirac's brackets, finally the results obtained are compared with those found in the literature.

Keywords: Topological theories; extra dimensions; Hamiltonian dynamics.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

This work was supported by CONACyT under Grant No. CB-2014-01/ 240781. We would like to thank R. Cartas-Fuentevilla for discussion on the subject and reading of the manuscript.

 

References

1. T. Matos and J. A. Nieto, Rev Mex. Fis. 39 (1993) S81-S131.         [ Links ]

2. M. Gogberashvili, A. H. Aguilar, D. M. Morejon and R. R. M. Luna, Phys. Lett. B 725 (2013) 208-211. arXiv:1202.1608.         [ Links ]

3. M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1986); J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998);         [ Links ] S. T. Yau (ed.), Mathemathical Aspects of String Theory (World Scientific, Singapore, 17 1987).         [ Links ]

4. A. Perez-Lorenzana, J. Phys. Conf. Ser. 18 (2005) 224.         [ Links ]

5. A. Muck, A. Pilaftsis and R. Ruckl, Phys. Rev. D 65 (2002) 085037.         [ Links ]

6. I. Antoniadis, Phys. Lett. B 246 (1990) 377.         [ Links ]

7. J.D. Lykken, Phys. Rev. D 54 (1996) 3693.         [ Links ]

8. K.R. Dienes, E. Dudas, and T. Gherghetta, Phys. Lett. B 436 (1998) 55;         [ Links ] Nucl. Phys. B 537 (1999) 47.         [ Links ]

9. L. Nilse, hep-ph/0601015.

10. G. Weiglein et al. (Physics Interplay of the LHC and the ILC), http://xxx.lanl.gov/abs/hep-ph/0410364arXiv:hep-ph/0410364.

11. H. Novales-Sanchez and J. J. Toscano, Phys. Rev. D 82 (2010) 116012.         [ Links ]

12. J. A. Nieto, J. Socorro and O. Obregon, Phys. Rev. Lett. 76 (1996) 3482; e-Print: gr-qc/9402029        [ Links ]

13. L. Freidel and A. Starodubtsev, Quantum gravity in terms of topological observables, preprint (2005), arXiv: hepth/0501191.

14. A. Escalante, Phys. Lett. B 676 (2009) 105-111.         [ Links ]

15. J. Govaerts, in Proc. Third Int. Workshop on Contemporary Problems in Mathematical Physics (COPROMAPH3 ), Cotonou (Republic of Benin), 1-7 November 2003.         [ Links ]

16. A. Escalante, J. Lopez-Osio, Int. J. Pure Appl. Math. 75 (2012) 339-352.         [ Links ]

17. A. Gaona, J. Antonio Garcia, Int. J. Mod. Phys. A 22 (2007) 851-867.         [ Links ]

18. K. Sundermeyer Constrained Dynamics, Lecture Notes in Physics vol. 169, Spinger-Verlag, Berlin Heidelberg New York, 1982.         [ Links ]

19. A. Escalante, J. Berra, Int. J. Pure Appl. Math. 79 (2012) 405423.         [ Links ]

20. M. Mondragon, M. Montesinos, J. Math. Phys. 47 (2006) 022301.         [ Links ]

21. A. Muck, A. Pilaftsis and R. Ruckl, Lect. Notes Phys. 647 (2004) 189.         [ Links ]

22. A. Escalante and I. Rubalcava, Int. J. Geom. Meth. Mod. Phys 9 (2012) 1250053.         [ Links ]

23. L. Castellani, Annals Phys. 143 (1982) 357.         [ Links ]

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

25. G. De los Santos and R. Linares, AIP Conf. Proc. 1256 (2010) 178.         [ Links ]

26. A. Escalante and M. Zarate, Annals of Phys, 353 (2015) 163178.         [ Links ]