Table of Contents
Journal of Gravity
Volume 2013, Article ID 812962, 5 pages
http://dx.doi.org/10.1155/2013/812962
Research Article

Is Einstein-Cartan Theory Coupled to Light Fermions Asymptotically Safe?

Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco No. 186, Col. Vicentina, 09340 México, DF, Mexico

Received 11 June 2013; Accepted 9 August 2013

Academic Editor: Kazuharu Bamba

Copyright © 2013 Eckehard W. Mielke. 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.

Linked References

  1. H. Weyl, “Gravitation and the electron,” Proceedings of the National Academy of Sciences of the United States of America, vol. 15, no. 4, pp. 323–334, 1929. View at Publisher · View at Google Scholar
  2. A. Trautman, “On the structure of the Einstein-Cartan equations,” in Differential Geometry, vol. 12 of Symposia Mathematica, pp. 139–1162, Academic Press, London, UK, 1973. View at Google Scholar
  3. É. Cartan, On Manifolds with an Affine Connection and the Theory of General Relativity, 1924, English translation of the French original, Bibliopolis, Napoli, Italy, 1986.
  4. F. W. Hehl, “Book review,” General Relativity and Gravitation, vol. 21, no. 3, pp. 315–317, 1989. View at Publisher · View at Google Scholar
  5. C. M. Will, “Finally, results from Gravity Probe B,” Physics, vol. 4, p. 43, 2011. View at Publisher · View at Google Scholar
  6. A. Trautman, “Spin and torsion may avert gravitational singularities,” Nature Physical Science, vol. 242, pp. 7–8, 1973. View at Google Scholar
  7. R. F. O'Connell, “Contact interactions in the Einstein and Einstein-Cartan-Sciama-Kibble (ECSK) theories of gravitation,” Physical Review Letters, vol. 37, no. 25, pp. 1653–1655, 1976. View at Publisher · View at Google Scholar · View at Scopus
  8. R. F. O'Connell, “Contact interactions in the Einstein and Einstein-Cartan-Sciama-Kibble (ECSK) theories of gravitation,” Physical Review Letters, vol. 38, no. 6, p. 298, 1977. View at Publisher · View at Google Scholar
  9. R. F. O'Connell, “Attractive spin-spin contact interactions in the Einstein-Cartan-Sciama-Kibble torsion theory of gravitation,” Physical Review D, vol. 16, no. 4, p. 1247, 1977. View at Google Scholar
  10. S. Weinberg, “Einstein's mistakes,” Physics Today, vol. 58, no. 11, pp. 31–35, 2005. View at Google Scholar
  11. S. Weinberg, “Weinberg replies,” Physics Today, vol. 59, p. 1516, 2006. View at Google Scholar
  12. F. W. Hehl and S. Weinberg, “Note on the torsion tensor,” Physics Today, vol. 60, no. 3, 2007. View at Publisher · View at Google Scholar
  13. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman, “Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance,” Physics Report, vol. 258, no. 1-2, pp. 1–171, 1995. View at Google Scholar · View at Scopus
  14. M. Blagojevic and F. W. Hehl, Eds., Gauge Theories of Gravitation: A Reader with Commentaries, Imperial College Press, London, UK, 2013.
  15. D. K. Wise, “MacDowell-Mansouri gravity and Cartan geometry,” Classical and Quantum Gravity, vol. 27, no. 15, Article ID 155010, pp. 1–26, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. H. F. Westman and T. G. Zlosnik, “Cartan gravity, matter fields, and the gauge principle,” Annals of Physics, vol. 334, pp. 157–197, 2013. View at Publisher · View at Google Scholar
  17. F. W. Hehl and B. K. Datta, “Nonlinear spinor equation and asymmetric connection in general relativity,” Journal of Mathematical Physics, vol. 12, no. 7, pp. 1334–1339, 1971. View at Google Scholar · View at Scopus
  18. E. W. Mielke and E. Sanchez Romero, “Cosmological evolution of a torsion-induced quintaxion,” Physical Review D, vol. 73, no. 4, Article ID 043521, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. V. S. Alves, M. Gomes, S. V. L. Pinheiro, and A. J. da Silva, “Four-fermion field theories and the Chern-Simons field: a renormalization group study,” Physical Review D, vol. 60, no. 2, pp. 1–4, 1999. View at Google Scholar · View at Scopus
  20. M. Reuter and F. Saueressig, “Quantum Einstein gravity,” New Journal of Physics, vol. 14, Article ID 055022, 2012. View at Google Scholar
  21. S. Weinberg, “Ultraviolet divergences in quantum theories of gravitation,” in General Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, Eds., chapter 16, p. 790, Cambridge University Press, 1979. View at Google Scholar
  22. E. W. Mielke, “Asymptotic safety of the Cartan induced four-fermion interaction?” in Proceedings of the Thirteenth Marcel Grossman Meeting on General Relativity, K. Rosquist, R. T. Jantzen, and R. Ruffini, Eds., pp. 1–3, World Scientific, Singapore, 2013. View at Google Scholar
  23. F. W. Hehl, J. Lemke, and E. W. Mielke, “Two lectures on fermions and gravity,” in Geometry and Theoretical Physics, J. Debrus and A. C. Hirshfeld, Eds., pp. 56–140, Springer, Berlin, Germany, 1991. View at Google Scholar
  24. J. Lemke, E. W. Mielke, and F. W. Hehl, “Äquivalenzprinzip für Materiewellen? Experimente mit Neutronen, Atomen, Neutrinos…,” Physik in unserer Zeit, vol. 25, no. 1, pp. 36–43, 1994. View at Publisher · View at Google Scholar
  25. E. W. Mielke, “Consistent coupling to Dirac fields in teleparallelism: comment on ‘metric-afflne approach to teleparallel gravity’,” Physical Review D, vol. 69, no. 12, Article ID 128501, 2004. View at Publisher · View at Google Scholar · View at Scopus
  26. D. Kreimer and E. W. Mielke, “Comment on ‘topological invariants, instantons, and the chiral anomaly on spaces with torsion’,” Physical Review D, vol. 63, no. 4, Article ID 048501, 2001. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Yajima and T. Kimura, “Anomalies in four-dimensional curved space with torsion,” Progress of Theoretical Physics, vol. 74, no. 4, pp. 866–880, 1985. View at Publisher · View at Google Scholar
  28. E. W. Mielke, “Anomalies and Gravity,” in Particles and Fields, Commemorative Volume of the Division of Particles and Fields of the Mexican Physical Society, Morelia, Michoacán, 6–12 November 2005, Part B, M. A. Pérez, L. F. Urrutia, and L. Villaseñor, Eds., vol. 857 of AIP Conference Proceedings, pp. 246–257, American Institute of Physics, Melville, NY, USA, 2006. View at Google Scholar
  29. E. W. Mielke, “Chern-Simons solutions of the chiral teleparallelism constraints of gravity,” Nuclear Physics B, vol. 622, no. 1-2, pp. 457–471, 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. E. W. Mielke, “Einstein-Weyl gravity from a topological SL(5, R) gauge invariant action,” Advances in Applied Clifford Algebras, vol. 22, pp. 803–817, 2012. View at Google Scholar
  31. E. W. Mielke, “Symmetry breaking in topological quantum gravity,” International Journal of Modern Physics D, vol. 22, no. 5, Article ID 1330009, 2013. View at Publisher · View at Google Scholar
  32. J.-E. Daum and M. Reuter, “Renormalization group flow of the Holst action,” Physics Letters B, vol. 710, no. 1, pp. 215–218, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. J.-E. Daum and M. Reuter, “Einstein-Cartan gravity, asymptotic safety, and the running Immirzi parameter,” Annals of Physics, vol. 334, pp. 351–419, 2013. View at Google Scholar
  34. E. W. Mielke, “Topologically modified teleparallelism, passing through the Nieh-Yan functional,” Physical Review D, vol. 80, Article ID 067502, 4 pages, 2009. View at Google Scholar
  35. E. W. Mielke, “Ashtekar's complex variables in general relativity and its teleparallelism equivalent,” Annals of Physics, vol. 219, no. 1, pp. 78–108, 1992. View at Google Scholar · View at Scopus
  36. R. D. Hecht, J. M. Nester, and V. V. Zhytnikov, “Some Poincaré gauge theory Lagrangians with well-posed initial value problems,” Physics Letters A, vol. 222, no. 1-2, pp. 37–42, 1996. View at Google Scholar · View at Scopus
  37. F.-H. Ho and J. M. Nester, “Poincaré gauge theory with coupled even and odd parity spin-0 modes: cosmological normal modes,” Annalen der Physik, vol. 524, no. 2, pp. 97–106, 2012. View at Publisher · View at Google Scholar · View at Scopus
  38. J. Bjorken, “Darkness: what comprises empty space?” Annalen der Physik, vol. 525, no. 5, pp. A67–A79, 2013. View at Google Scholar
  39. K. Falls, D. F. Litim, K. Nikolakopoulos, and C. Rahmede, “A bootstrap towards asymptotic safety,” http://arxiv.org/abs/1301.4191.
  40. F. E. Schunck, F. V. Kusmartsev, and E. W. Mielke, “Dark matter problem and effective curvature Lagrangians,” General Relativity and Gravitation, vol. 37, no. 8, pp. 1427–1433, 2005. View at Publisher · View at Google Scholar · View at Scopus
  41. R. Kuhfuss and J. Nitsch, “Propagating modes in gauge field theories of gravity,” General Relativity and Gravitation, vol. 18, no. 12, pp. 1207–1227, 1986. View at Publisher · View at Google Scholar · View at Scopus
  42. C.-Y. Lee and Y. Ne'eman, “Renormalization of gauge-affine gravity,” Physics Letters B, vol. 242, no. 1, pp. 59–63, 1990. View at Google Scholar · View at Scopus
  43. A. Eichhorn and H. Gies, “Light fermions in quantum gravity,” New Journal of Physics, vol. 13, Article ID 125012, 2011. View at Publisher · View at Google Scholar · View at Scopus
  44. M.-J. Schwindt and C. Wetterich, “Asymptotically free four-fermion interactions and electroweak symmetry breaking,” Physical Review D, vol. 81, no. 5, Article ID 055005, 2010. View at Publisher · View at Google Scholar · View at Scopus
  45. F. Bazzocchi, M. Fabbrichesi, R. Percacci, A. Tonero, and L. Vecchi, “Fermions and Goldstone bosons in an asymptotically safe model,” Physics Letters B, vol. 705, no. 4, pp. 388–392, 2011. View at Publisher · View at Google Scholar · View at Scopus
  46. D. Benedetti and S. Speziale, “Perturbative quantum gravity with the Immirzi parameter,” Journal of High Energy Physics, vol. 2011, no. 6, article 107, 2011. View at Publisher · View at Google Scholar · View at Scopus
  47. R. Hojman, C. Mukku, and W. A. Sayed, “Parity violation in metric-torsion theories of gravitation,” Physical Review D, vol. 22, no. 8, pp. 1915–1921, 1980. View at Publisher · View at Google Scholar · View at Scopus
  48. Y. N. Obukhov and F. W. Hehl, “Extended Einstein-Cartan theory a la Diakonov: the field equations,” Physics Letters B, vol. 713, p. 321, 2012. View at Google Scholar
  49. N. J. Popławski, “Four-fermion interaction from torsion as dark energy,” General Relativity and Gravitation, vol. 44, no. 2, pp. 491–499, 2012. View at Publisher · View at Google Scholar · View at Scopus
  50. I. B. Khriplovich, “Gravitational four-fermion interaction on the Planck scale,” Physics Letters B, vol. 709, no. 3, pp. 111–113, 2012. View at Publisher · View at Google Scholar · View at Scopus
  51. I. B. Khriplovich and A. S. Rudenko, “Cosmology constrains gravitational four-fermion interaction,” Journal of Cosmology and Astroparticle Physics, vol. 2012, article 040, 2012. View at Publisher · View at Google Scholar
  52. H. Nicolai, “Quantum gravity: the view from particle physics,” http://arxiv.org/abs/1301.5481.