Thoughts on duality and fundamental constants
J.A. Nieto*, L. Ruiz, and J. Silvas
Facultad de Ciencias Físico–Matemáticas, Universidad Autónoma de Sinaloa, 80000, Culiacán, Sinaloa, México,
*e–mail: nieto@uas.uasnet.mx
Recibido el 13 de septiembre de 2006 ]]> Aceptado el 18 de enero de 2007
Abstract
We consider some fundamental constants from the point of view of the duality symmetry. Our analysis of duality is focused on three issues: the maximum radiated power of gravitational waves, the cosmological constant, and the magnetic monopole mass. We show that the maximum radiated power of gravitational waves implies that the Planck time is a minimal time. Furthermore, we prove that duality implies a quantization of the cosmological constant. Finally, by using one of the Euler series for the number π, we show that the Dirac electric–magnetic charge quantization implies a mass for the magnetic monopole (or neutrino) of the order of 10–5 the mass of the electron.
Keywords: Fundamental constants; gravitational waves; cosmological constant; duality.
Resumen
Consideramos algunas constantes fundamentales desde el punto de vista de la simetría de dualidad. Nuestro análisis de dualidad se enfoca en tres temas: la potencia máxima radiada de ondas gravitacionales, la constante cosmológica y la masa del monopolo magnético. Demostramos que la potencia máxima radiada de ondas gravitacionales implica que el tiempo de Planck corresponde a un tiempo mínimo. Mas aún, probamos que la dualidad implica una cuantización de la constante cosmológica. Finalmente, usando una de las series de Euler para el numero π, demostramos que la cuantización de la carga eléctrica–magnética de Dirac implica una masa para el monopolo magnético (o neutrino) del orden de 10–5 la masa del electrón.
Descriptores: Constantes fundamentales; ondas gravitacionales; constante cosmológica; dualidad.
]]> PACS: 04.60.–m; 04.30.–w; 6.20.Jr; 98.80.–k
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Acknowledgments
This work was supported in part by the UAS under the program PROFAPI–2006.
References
1. M.J. Duff, L.B. Okun, and G. Veneziano, JHEP 0203 (2002) 023; physics/0110060. [ Links ]
2. M.J. Duff, "Comments on Time Variation of Fundamental Constants", hep–th/0208093. [ Links ]
3. P.A.M. Dirac, Nature 139 (1937). [ Links ]
4. J.A. Nieto, Phys. Lett. A 262 (1999) 274; hep–th/9910049. [ Links ]
5. G.F.R. Ellis and J.P. Uzan, Am. J. Phys. 73 (2005) 240; gr–qc/0305099. [ Links ]
6. G. Veneziano, "Physics with a Fundamental Length", in Memorial Volume dedicated to Dima Knizhnik. In *Brink, L. (ed.) et al.: Physics and mathematics of strings* 509–529 and CERN Geneva – TH. 5581 (89,rec.Jan.90) 20 p. [ Links ]
7. T. Padmanabhan, Gen. Rel. Grav. 17 (1985) 215; see also W.M. Saslow, Eur. J. Phys. 19 (1998) 313. [ Links ]
8. B.S. DeWitt, Gravitation, An introduction to current research, ed. by L. Witten (Wiley, New York, 1962). [ Links ]
9. L. Rosenfeld, Selected papers of Leon Rosenfeld, ed. by R.S. Cohen and J.J. Stachel (Reidel, Dordrecht, 1966). [ Links ]
10. E. Prugovecki, Found. Phys. 26 (1996) 1645; gr–qc/9603044; see also H.H. von Borzeskowski and H.J. Treder, The Meaning of Quantum Gravity (Reidel, Dordrecht, 1988). [ Links ]
11. L.J. Garay, Int. J. Mod. Phys. A 10 (1995) 145; gr–qc/9403008. [ Links ]
12. A. Zee, Phys. Rev. Lett. 55 (1985) 2379; Erratum–ibid. 56 (1986) 1101. [ Links ]
13. C. Castro, Found. Phys. 34 (2004) 1091. [ Links ]
14. M.J. Duff, "Progress in M–Theory", Prepared for 23rd Annual MRST (Montreal–Rochester–Syracuse–Toronto) Conference on High–Energy Physics (MRST 2001), London, Ontario, Canada, 16–18 May 2001. Published in *London 2001, Theoretical high energy physics* 3–18 Also in *Fort Lauderdale 2001, Cosmology and elementary particle physics* 245–254 Also in *Cairo 2001, High energy physics* 103–117 M–theory. [ Links ]
15. J.A. Nieto, Rev. Mex. Fis. 44 (1998) 358; hep–th/9807107. [ Links ]
16. J.A. Nieto and M.C. Marín, J. Math. Phys. 41 (2000) 7997; hep–th/0005117. [ Links ]
17. J.A. Nieto, J. Math. Phys. 45 (2004) 285; hep–th/0212100. [ Links ]
18. J.A. Nieto and M.C. Marín, Int. J. Mod. Phys. A 18 (2003) 5261; hep–th/0302193. [ Links ]
19. J.A. Nieto, Adv. Theor. Math. Phys. 8 (2004) 177; hep–th/0310071. [ Links ]
20. J.A. Nieto, Rev. Mex. Fis. E 51 (2005) 5; hep–th/0407093. [ Links ]
21. J.A. Nieto, Adv. Theor. Math. Phys. 10 (2006) 747; hep–th/0506106. [ Links ]
22. J.A. Nieto, "Toward a Connection Between the Oriented Matroid Theory and Supersymmetry", hep–th/0510185. [ Links ]
23. A. Bjorner, M. Las Vergnas, B. Sturmfels, N. White, and G. M. Ziegler, Oriented Martroids (Cambridge University Press, Cambridge, 1993). [ Links ]
24. H. Ertel, Sitzungsberichte Preussische Akademie der Wissenschaften, Phys. Math. Klasse, 1 (1935) 3; [ Links ]Naturwissenschaften, 23 (1935) 36; [ Links ]Naturwissenschaften 23 (1935) 70; [ Links ]Physikalische Zeitschrift 37 (1936) 138. [ Links ]
25. W. Schroder and H.J. Treder, Found. Phys. 28 (1998) 1013. [ Links ]
26. C.M. Hull, Nucl. Phys. B 583 (2000) 237; hep–th/0004195. [ Links ]
27. I. Moss, Phys. Lett. B 283 (1992) 52. [ Links ]
28. A Pinzul and A. Stern, Class. Quant. Grav. 23 (2006) 1009; hep–th/0511071. [ Links ]
29. H. Casini, R. Montemayor and L.F. Urrutia, Phys. Rev. D 68 (2003) 065011; hep–th/0304228. [ Links ] ]]>