Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2017, Article ID 4768341, 8 pages
https://doi.org/10.1155/2017/4768341
Research Article

Effective Models of Quantum Gravity Induced by Planck Scale Modifications in the Covariant Quantum Algebra

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, Urca, 22290-180 Rio de Janeiro, RJ, Brazil
2Instituto Federal do Espírito Santo (IFES), Av. Vitória 1729, Jucutuquara, 29040-780 Vitória, ES, Brazil
3Departamento de Matemática, Física e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra, Km 298, Polo Industrial, 27537-000 Resende, RJ, Brazil

Correspondence should be addressed to G. P. de Brito; moc.liamg@inizzapovatsug

Received 26 May 2017; Accepted 13 August 2017; Published 26 September 2017

Academic Editor: Angel Ballesteros

Copyright © 2017 G. P. de Brito et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. R. P. Woodard, “How far are we from the quantum theory of gravity?” Reports on Progress in Physics, vol. 72, no. 12, Article ID 126002, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Carlip, “Quantum gravity: a progress report,” Reports on Progress in Physics, vol. 64, no. 8, pp. 885–942, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  3. I. L. Buchbinder, S. D. Odintsov, and I. L. Shapiro, Effective Action in Quantum Gravity, IOP Publishing, Bristol, England, 1992. View at MathSciNet
  4. K. S. Stelle, “Renormalization of higher-derivative quantum gravity,” Physical Review. D. Particles and Fields. Third Series, vol. 16, no. 4, pp. 953–969, 1977. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. L. Modesto, “Super-renormalizable multidimensional quantum gravity,” Astron. Rev, vol. 8, pp. 4–33, 2013. View at Google Scholar
  6. M. Asorey, J. L. Lopez, and I. L. Shapiro, “Particles and Fields; Gravitation; Cosmology,” International Journal of Modern Physics A, vol. 12, no. 32, pp. 5711–5734, 1997. View at Publisher · View at Google Scholar
  7. L. Modesto, “Super-renormalizable Quantum Gravity,” Physical Review D, vol. 86, no. 4, Article ID 044005, 2012. View at Publisher · View at Google Scholar
  8. P. Donà, S. Giaccari, L. Modesto, L. Rachwal, and Y. Zhu, “Scattering amplitudes in super-renormalizable gravity,” Journal of High Energy Physics, vol. 2015, no. 8, article no. 38, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Modesto and L. Rachwal, “Super-renormalizable and finite gravitational theories,” Nuclear Physics B, vol. 889, pp. 228–248, 2014. View at Publisher · View at Google Scholar
  10. T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, “Towards singularity- and ghost-free theories of gravity,” Physical Review Letters, vol. 108, no. 3, Article ID 031101, 4 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Accioly, J. Helayel-Neto, E. Scatena, and R. Turcati, “Solving the riddle of the incompactibility between renormalizability and unitarity in N-dimensional Einstein gravity enlarged by curvature-squared terms,” Int. J. Mod. Phys. D, vol. 22, Article ID 1342015, 2013. View at Google Scholar
  12. M. Maggiore, “A generalized uncertainty principle in quantum gravity,” Physics Letters B, vol. 304, no. 1-2, pp. 65–69, 1993. View at Publisher · View at Google Scholar
  13. H. S. Snyder, “Quantized space-time,” Physical Review, vol. 71, no. 1, pp. 38–41, 1947. View at Publisher · View at Google Scholar
  14. N. Seiberg and E. Witten, “String theory and noncommutative geometry,” Journal of High Energy Physics, vol. 1999, no. 09, article 032, 1999. View at Publisher · View at Google Scholar
  15. S. Hossenfelder, “Minimal length scale scenarios for quantum gravity,” Living Reviews in Relativity, vol. 16, no. 2, 2013. View at Publisher · View at Google Scholar
  16. M. Reuter and J. M. Schwindt, “A minimal length from the cutoff modes in asymptotically safe quantum gravity,” Journal of High Energy Physics, vol. 2006, no. 1, p. 70, 2006. View at Publisher · View at Google Scholar
  17. R. Percacci and G. P. Vacca, “Asymptotic safety, emergence and minimal length,” Classical and Quantum Gravity, vol. 27, no. 24, Article ID 245026, 245026, 16 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. Kempf, “Non-pointlike particles in harmonic oscillators,” Journal of Physics. A. Mathematical and General, vol. 30, no. 6, pp. 2093–2101, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. F. Brau, “Minimal length uncertainty relation and the hydrogen atom,” Journal of Physics. A. Mathematical and General, vol. 32, no. 44, pp. 7691–7696, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, “Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations,” Physical Review D, vol. 65, Article ID 125027, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  21. S. Benczik, L. N. Chang, D. Minic, and T. Takeuchi, “Hydrogen-atom spectrum under a minimal-length hypothesis,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 72, no. 1, Article ID 012104, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Pramanik, M. Moussa, M. Faizal, and A. F. Ali, “Path integral quantization corresponding to the deformed Heisenberg algebra,” Annals of Physics, vol. 362, pp. 24–35, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. Faizal and M. M. Khalil, “GUP-corrected thermodynamics for all black objects and the existence of remnants,” Int. J. Mod. Phys. A, vol. 30, Article ID 1550144, 2015. View at Google Scholar
  24. M. Faizal and S. I. Kruglov, “Deformation of the Dirac equation,” Int. J. Mod. Phys. D, vol. 25, Article ID 1650013, 2015. View at Google Scholar
  25. C. Quesne and V. M. Tkachuk, “Lorentz-covariant deformed algebra with minimal length and application to the (1 + 1)-dimensional Dirac oscillator,” Journal of Physics A: Mathematical and General, vol. 39, no. 34, article no. 021, pp. 10909–10922, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. C. Quesne and V. M. Tkachuk, “Lorentz-covariant deformed algebra with minimal length,” Czechoslovak Journal of Physics, vol. 56, no. 10-11, pp. 1269–1274, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. S. K. Moayedi, M. R. Setare, and H. Moayeri, “Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length,” International Journal of Theoretical Physics, vol. 49, no. 9, pp. 2080–2088, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. S. K. Moayedi, M. R. Setare, H. Moayeri, and M. Poorakbar, “Formulation of the spinor field in the presence of a minimal length based on the Quesnetkachuk algebra,” International Journal of Modern Physics A, vol. 26, no. 29, pp. 4981–4990, 2011. View at Publisher · View at Google Scholar · View at Scopus
  29. S. K. Moayedi, M. R. Setare, and H. Moayeri, “Formulation of an electrostatic field with a charge density in the presence of a minimal length based on the Kempf algebra,” A Letters Journal Exploring the Frontiers of Physics, vol. 98, Article ID 50001, 2012. View at Publisher · View at Google Scholar
  30. S. K. Moayedi, M. R. Setare, and B. Khosropour, “Lagrangian formulation of a magnetostatic field in the presence of a minimal length scale based on the Kempf algebra,” Int. J. Mod. Phys. A, vol. 28, Article ID 1350142, 2013. View at Google Scholar
  31. S. K. Moayedi, M. R. Setare, and B. Khosropour, “Formulation of electrodynamics with an external source in the presence of a minimal measurable length,” Advances in High Energy Physics, vol. 2013, Article ID 657870, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. A. V. Silva, E. M. C. Abreu, and M. J. Neves, “Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale,” Int. J. Mod. Phys. A, vol. 31, Article ID 1650096, 2016. View at Google Scholar
  33. M. Dias, H. da Silva, and J. M. E. Scatena, “Higher-order theories from the minimal length,” Int. J. Mod. Phys. A, vol. 31, Article ID 1650087, 2016. View at Google Scholar
  34. M. Faizal, “Supersymmetry breaking as a new source for the generalized uncertainty principle,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 757, pp. 244–246, 2016. View at Publisher · View at Google Scholar · View at Scopus
  35. P. Pedram, “A higher order GUP with minimal length uncertainty and maximal momentum,” Physics Letters B, vol. 714, no. 2-5, pp. 317–323, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. P. Pedram, “A higher order GUP with minimal length uncertainty and maximal momentum II: applications,” Physics Letters B, vol. 718, no. 2, pp. 638–645, 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. A. Accioly, A. Azeredo, and H. Mukai, “Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions,” Journal of Mathematical Physics, vol. 43, no. 1, pp. 473–491, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  38. V. Kuksa, “Complex-mass definition and the structure of unstable particle's propagator,” Adv. High Energy Phys, vol. 2015, Article ID 490238, 2015. View at Google Scholar
  39. R. Turcati and M. J. Neves, “Complex-mass shell renormalization of the higher-derivative electrodynamics,” The European Physical Journal C, vol. 76, no. 8, 2016. View at Publisher · View at Google Scholar
  40. H. Yamamoto, “Convergent field theory with complex masses,” Progress of Theoretical Physics, vol. 42, p. 707, 1969. View at Google Scholar
  41. H. Yamamoto, “Convergent field theory with complex masses. 2. quantization and scattering matrix,” Progress of Theoretical Physics, vol. 43, p. 520, 1970. View at Google Scholar
  42. H. Yamamoto, “Observability of complex ghosts and tachyons,” Progress of Theoretical Physics, vol. 55, p. 1998, 1976. View at Google Scholar
  43. L. Modesto, “Super-renormalizable or finite Lee-Wick quantum gravity,” Nuclear Physics. B. Theoretical, Phenomenological, and Experimental High Energy Physics. Quantum Field Theory and Statistical Systems, vol. 909, pp. 584–606, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. L. Modesto and I. L. Shapiro, “Superrenormalizable quantum gravity with complex ghosts,” Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology, vol. 755, pp. 279–284, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. A. Accioly, J. Helayël-Neto, F. E. Barone, and W. Herdy, “Simple prescription for computing the interparticle potential energy for,” Classical and Quantum Gravity, vol. 32, no. 3, p. 035021, 2015. View at Publisher · View at Google Scholar
  46. L. Modesto, T. Paula Netto, and I. L. Shapiro, “On Newtonian singularities in higher derivative gravity models,” Journal of High Energy Physics, vol. 04, p. 098, 2015. View at Google Scholar
  47. B. L. Giacchini, “On the cancellation of Newtonian singularities in higher-derivative gravity,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 766, pp. 306–311, 2017. View at Publisher · View at Google Scholar · View at Scopus
  48. G. Narain and R. Anishetty, “Short distance freedom of quantum gravity,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 711, no. 1, pp. 128–131, 2012. View at Publisher · View at Google Scholar · View at Scopus
  49. B. Majumder, “Quantum black hole and the modified uncertainty principle,” Physics Letters B, vol. 701, no. 4, pp. 384–387, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  50. C. Bambi, L. Modesto, and Y. Wang, “Lee-Wick black holes,” Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology, vol. 764, pp. 306–309, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  51. L. Modesto and L. Rachwal, “Nonlocal quantum gravity: a review,” Int.J.Mod.Phys. D, vol. 26, Article ID 1730020, 2017. View at Google Scholar