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Varying electric charge in multiscale spacetimes

Gianluca Calcagni1,*, João Magueijo2,3,†, and David Rodríguez Fernández4,‡

  • 1Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain
  • 2Theoretical Physics, Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
  • 3Dipartimento di Fisica, Università La Sapienza and Sez. Roma1 INFN, Piazzale A. Moro 2, 00185 Roma, Italia
  • 4Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain

  • *calcagni@iem.cfmac.csic.es
  • †magueijo@ic.ac.uk
  • ‡davidrodriguezfernandez@estumail.ucm.es
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Phys. Rev. D 89, 024021 – Published 13 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.024021

Abstract

We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying-coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multifractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion.

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References (127)

  1. G. ’t Hooft, in Salamfestschrift, edited by A. Ali, J. Ellis, and S. Randjbar-Daemi (World Scientific, Singapore, 1993).
  2. S. Carlip, AIP Conf. Proc. 1196, 72 (2009).
  3. G. Calcagni, Phys. Rev. Lett. 104, 251301 (2010).
  4. G. Calcagni, Phys. Rev. D 84 061501(R) (2011).
  5. G. Calcagni, Phys. Rev. D 86, 044021 (2012).
  6. G. Calcagni, AIP Conf. Proc. 1483, 31 (2012).
  7. G. Calcagni and G. Nardelli, Phys. Rev. D 87, 085008 (2013).
  8. D. J. Shaw and J. D. Barrow, Phys. Lett. B 639, 596 (2006).
  9. J. D. Barrow and D. J. Shaw, Gen. Relativ. Gravit. 39, 1235 (2007).
  10. J.-P. Uzan, Living Rev. Relativity 14, 2 (2011).
  11. J. D. Barrow, Ann. Phys. (Berlin) 19, 202 (2010).
  12. T. Chiba, Prog. Theor. Phys. 126, 993 (2011).
  13. C. Orzel, Phys. Scr. 86, 068101 (2012).
  14. P. A. R. Ade et al. (Planck Collaboration), arXiv:1303.5076.
  15. M. J. Drinkwater, J. K. Webb, J. D. Barrow, and V. V. Flambaum, Mon. Not. R. Astron. Soc. 295, 457 (1998).
  16. C. L. Carilli, K. M. Menten, J. T. Stocke, E. Perlman, R. Vermeulen, F. Briggs, A. G. de Bruyn, J. Conway, and C. P. Moore, Phys. Rev. Lett. 85, 5511 (2000); 86, 1910(E) (2001).
  17. M. T. Murphy, J. K. Webb, V. V. Flambaum, M. J. Drinkwater, F. Combes, and T. Wiklind, Mon. Not. R. Astron. Soc. 327, 1244 (2001).
  18. M. T. Murphy, J. K. Webb, and V. V. Flambaum, Mon. Not. R. Astron. Soc. 345, 609 (2003).
  19. M. T. Murphy, V. V. Flambaum, J. K. Webb, V. V. Dzuba, J. X. Prochaska, and A. M. Wolfe, Lect. Notes Phys. 648, 131 (2004).
  20. J. A. King, D. J. Mortlock, J. K. Webb, and M. T. Murphy, Mem. S.A.It. 80, 864 (2009).
  21. H. Chand, R. Srianand, P. Petitjean, and B. Aracil, Astron. Astrophys. 417, 853 (2004).
  22. R. Srianand, H. Chand, P. Petitjean, and B. Aracil, Phys. Rev. Lett. 92, 121302 (2004).
  23. M. T. Murphy, J. K. Webb, and V. V. Flambaum, Mon. Not. R. Astron. Soc. 384, 1053 (2008).
  24. M. T. Murphy, J. K. Webb, and V. V. Flambaum, Phys. Rev. Lett. 99, 239001 (2007).
  25. R. Srianand, H. Chand, P. Petitjean, and B. Aracil, Phys. Rev. Lett. 99, 239002 (2007).
  26. J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, and M. B. Bainbridge, Phys. Rev. Lett. 107, 191101 (2011).
  27. J. A. King, J. K. Webb, M. T. Murphy, V. V. Flambaum, R. F. Carswell, M. B. Bainbridge, M. R. Wilczynska, and F. E. Koch, Mon. Not. R. Astron. Soc. 422, 3370 (2012).
  28. P. Molaro et al., Astron. Astrophys. 555, A68 (2013).
  29. H. Rahmani, R. Srianand, N. Gupta, P. Petitjean, P. Noterdaeme, and D. A. Vasquez, Mon. Not. R. Astron. Soc. 425, 556 (2012).
  30. S. A. Levshakov, F. Combes, F. Boone, I. I. Agafonova, D. Reimers, and M. G. Kozlov, Astron. Astrophys. 540, L9 (2012).
  31. E. Cameron and T. Pettitt, arXiv:1207.6223.
  32. J. C. Berengut, V. V. Flambaum, A. Ong, J. K. Webb, J. D. Barrow, M. A. Barstow, S. P. Preval, and J. B. Holberg, Phys. Rev. Lett. 111, 010801 (2013).
  33. G. Calcagni and G. Nardelli, Adv. Theor. Math. Phys. 16, 1315 (2012).
  34. G. Calcagni, G. Nardelli, and M. Scalisi, J. Math. Phys. (N.Y.) 53, 102110 (2012).
  35. G. Calcagni, Adv. Theor. Math. Phys. 16, 549 (2012).
  36. F.-Y. Ren, Z.-G. Yu, and F. Su, Phys. Lett. A 219, 59 (1996).
  37. Z.-G. Yu, F.-Y. Ren, and J. Zhou, J. Phys. A 30, 5569 (1997).
  38. F.-Y. Ren, Z.-G. Yu, J. Zhou, A. Le Méhauté, and R. R. Nigmatullin, Physica (Amsterdam) 246A, 419 (1997).
  39. Z.-G. Yu, Phys. Lett. A 257, 221 (1999).
  40. W.-Y. Qiu and J. Lü, Phys. Lett. A 272, 353 (2000).
  41. F.-Y. Ren, W.-Y. Qiu, J.-R. Liang, and X.-T. Wang, Phys. Lett. A 288, 79 (2001).
  42. F.-Y. Ren, J.-R. Liang, X.-T. Wang, and W.-Y. Qiu, Chaos Solitons Fractals 16, 107 (2003).
  43. R. R. Nigmatullin and A. Le Méhauté, J. Non-Cryst. Solids 351, 2888 (2005).
  44. G. Calcagni, J. High Energy Phys. 01 (2012) 065.
  45. G. Calcagni, Phys. Rev. E 87, 012123 (2013).
  46. M. Arzano, G. Calcagni, D. Oriti, and M. Scalisi, Phys. Rev. D 84, 125002 (2011).
  47. G. Calcagni and G. Nardelli, Phys. Rev. D 88, 124025 (2013).
  48. S. I. Muslih, M. Saddallah, D. Baleanu, and E. Rabei, Romanian Journal of Physics 55, 659 (2010).
  49. F. H. Stillinger, J. Math. Phys. (N.Y.) 18, 1224 (1977).
  50. C. Palmer and P. N. Stavrinou, J. Phys. A 37, 6987 (2004).
  51. M. Zubair, M. J. Mughal, and Q. A. Naqvi, Prog. Electromagn. Res. Lett. 19, 137 (2010).
  52. M. Zubair, M. J. Mughal, Q. A. Naqvi, and A. A. Rizvi, Prog. Electromagn. Res. 114, 255 (2011).
  53. M. Zubair, M. J. Mughal, and Q. A. Naqvi, Prog. Electromagn. Res. 114, 443 (2011).
  54. M. Zubair, M. J. Mughal, and Q. A. Naqvi, Nonlinear Anal.: Real World Appl. 12, 2844 (2011).
  55. M. Zubair, M. J. Mughal, and Q. A. Naqvi, J. Electromagn. Waves Appl. 25, 1481 (2011).
  56. L. Nottale, Fractal Space-Time and Micro-Physics: Towards a Theory of Scale Relativity (World Scientific, Singapore, 1993).
  57. L. Nottale, Chaos Solitons Fractals 7, 877 (1996).
  58. L. Nottale, Foundations of Science 15, 101 (2010).
  59. L. Nottale, in Relativity in General, edited by J. Diaz Alonso and M. Lorente Paramo (Editions Frontières, Paris, 1994).
  60. L. Nottale, Electromagn. Phen. 3, 92 (2003).
  61. L. Nottale, M.-N. Célérier, and T. Lehner, J. Math. Phys. (N.Y.) 47, 032303 (2006).
  62. G. Calcagni, Int. J. Mod. Phys. A 28, 1350092 (2013).
  63. V. E. Tarasov, Phys. Plasmas 12, 082106 (2005).
  64. V. E. Tarasov, Mod. Phys. Lett. B 19, 1107 (2005).
  65. V. E. Tarasov, Mod. Phys. Lett. A 21, 1587 (2006).
  66. V. E. Tarasov, Phys. Plasmas 13, 052107 (2006).
  67. N. Engheta, J. Electromagn. Waves Appl. 9, 1179 (1995).
  68. N. Engheta, IEEE Trans. Antennas Propag. 44, 1565 (1996).
  69. N. Engheta, IEEE Antennas Prop. Mag. 39, 35 (1997).
  70. N. Engheta, Microwave Opt. Technol. Lett. 17, 86 (1998).
  71. N. Engheta, Microwave Opt. Technol. Lett. 21, 338 (1999).
  72. A. Lakhtakia, Microwave Opt. Technol. Lett. 28, 385 (2001).
  73. E. I. Veliev and N. Engheta, in Proceedings of 10th International Conference on Mathematical Methods in Electromagnetic Theory (IEEE, New York, 2004), p. 228.
  74. M. V. Ivakhnychenko and E. I. Veliev, in Proceedings of 10th International Conference on Mathematical Methods in Electromagnetic Theory (IEEE, New York, 2004), p. 231.
  75. Q. A. Naqvi and M. Abbas, Opt. Commun. 241, 349 (2004).
  76. S. A. Naqvi, Q. A. Naqvi, and A. Hussain, Opt. Commun. 266, 404 (2006).
  77. A. Hussain and Q. A. Naqvi, Prog. Electromagn. Res. 59, 199 (2006).
  78. A. Hussain, S. Ishfaq, and Q. A. Naqvi, Prog. Electromagn. Res. 63, 319 (2006).
  79. S. I. Muslih and D. Baleanu, Nonlinear Anal.: Real World Appl. 8, 198 (2007).
  80. V. E. Tarasov, Theor. Math. Phys. 158, 355 (2009).
  81. V. E. Tarasov, Ann. Phys. (Amsterdam) 323, 2756 (2008).
  82. D. Baleanu, A. K. Golmankhaneh, and A. K. Golmankhaneh, Nonlinear Anal.: Real World Appl. 11, 288 (2010).
  83. A. Hussain, S. A. Naqvi, A. Illahi, and Q. A. Naqvi, arXiv:1109.1917.
  84. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, London, 1980).
  85. B. Zwiebach, A First Course in String Theory (Cambridge University Press, Cambridge, England, 2009).
  86. H. B. Sandvik, J. D. Barrow, and J. Magueijo, Phys. Rev. Lett. 88, 031302 (2002).
  87. J. Collins, Renormalization (, Cambridge, England, 1984).
  88. J. D. Bekenstein, Phys. Rev. D 25, 1527 (1982).
  89. J. D. Barrow and C. O’Toole, Mon. Not. R. Astron. Soc. 322, 585 (2001).
  90. J. Magueijo, H. B. Sandvik, and T. W.B. Kibble, Phys. Rev. D 64, 023521 (2001).
  91. J. D. Bekenstein, Phys. Rev. D 66, 123514 (2002).
  92. J. D. Barrow, H. B. Sandvik, and J. Magueijo, Phys. Rev. D 65, 063504 (2002).
  93. K. A. Olive and M. Pospelov, Phys. Rev. D 65, 085044 (2002).
  94. J. D. Barrow, J. Magueijo, and H. B. Sandvik, Phys. Rev. D 66, 043515 (2002).
  95. D. F. Mota and J. D. Barrow, Phys. Lett. B 581, 141 (2004).
  96. D. Kimberly and J. Magueijo, Phys. Lett. B 584, 8 (2004).
  97. D. J. Shaw and J. D. Barrow, Phys. Rev. D 71, 063525 (2005).
  98. N. Chamoun, S. J. Landau, and H. Vucetich, Phys. Lett. B 504, 1 (2001).
  99. X. Calmet and H. Fritzsch, Eur. Phys. J. C 24, 639 (2002).
  100. P. Langacker, G. Segrè, and M. J. Strassler, Phys. Lett. B 528, 121 (2002).
  101. M. Dine, Y. Nir, G. Raz, and T. Volansky, Phys. Rev. D 67, 015009 (2003).
  102. T. Banks, M. Dine, and M. R. Douglas, Phys. Rev. Lett. 88, 131301 (2002).
  103. J. Magueijo, Rep. Prog. Phys. 66, 2025 (2003).
  104. J. W. Moffat, Int. J. Mod. Phys. D 02, 351 (1993).
  105. A. Albrecht and J. Magueijo, Phys. Rev. D 59, 043516 (1999).
  106. J. D. Barrow and J. Magueijo, Phys. Lett. B 443, 104 (1998).
  107. J. D. Barrow and J. Magueijo, Phys. Lett. B 447, 246 (1999).
  108. J. D. Barrow and J. Magueijo, Classical Quantum Gravity 16, 1435 (1999).
  109. J. D. Barrow, Phys. Rev. D 59, 043515 (1999).
  110. S. Landau, P. D. Sisterna, and H. Vucetich, Phys. Rev. D 63, 081303(R) (2001).
  111. G. F. R. Ellis and J.-P. Uzan, Am. J. Phys. 73, 240 (2005).
  112. J. Magueijo, Phys. Rev. D 62, 103521 (2000).
  113. J. Magueijo, J. D. Barrow, and H. B. Sandvik, Phys. Lett. B 549, 284 (2002).
  114. J. Magueijo, Phys. Rev. Lett. 100, 231302 (2008).
  115. J. Magueijo, Phys. Rev. D 79, 043525 (2009).
  116. J. Magueijo, J. Noller, and F. Piazza, Phys. Rev. D 82, 0435251 (2010).
  117. J. Magueijo, Classical Quantum Gravity 25, 202002 (2008).
  118. K. Sigurdson, A. Kurylov, and M. Kamionkowski, Phys. Rev. D 68, 103509 (2003).
  119. P. Hořava, Phys. Rev. D 79, 084008 (2009).
  120. P. Hořava, Phys. Rev. Lett. 102, 161301 (2009).
  121. T. Damour and A. M. Polyakov, Nucl. Phys. B423, 532 (1994).
  122. G. R. Dvali and M. Zaldarriaga, Phys. Rev. Lett. 88, 091303 (2002).
  123. K. A. Olive and M. Pospelov, Phys. Rev. D 77, 043524 (2008).
  124. G. Calcagni, J. High Energy Phys. 03 (2010) 120.
  125. G. Calcagni, J. Cosmol. Astropart. Phys. 12 (2013) 041.
  126. P. P. Avelino, S. Esposito, G. Mangano, C. J. A. P. Martins, A. Melchiorri, G. Miele, O. Pisanti, G. Rocha, and P. Viana, Phys. Rev. D 64, 103505 (2001).
  127. K. A. Olive, M. Peloso, and J.-P. Uzan, Phys. Rev. D 83, 043509 (2011).

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Phys. Rev. D 89, 024021– Published 13 January, 2014
  • Received 28 October 2013

© 2014 American Physical Society

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