Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Quantum gravitational contributions to quantum electrodynamics

Nature volume 468, pages 56–59 (2010)Cite this article

Subjects

Abstract

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. However, that claim has been very controversial and the matter has not been settled. Here I report an analysis (free from the earlier controversies) demonstrating that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the electric charge vanishing at high energies, a result known as asymptotic freedom.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. Gross, D. & Wilczek, F. Ultraviolet behavior of non-Abelian gauge theories. Phys. Rev. Lett. 30, 1343–1346 (1973)

    Article  ADS  CAS  Google Scholar 

  2. Politzer, D. Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30, 1346–1349 (1973)

    Article  ADS  CAS  Google Scholar 

  3. Callan, C. G. Broken scale invariance in scalar field theory. Phys. Rev. D 2, 1541–1547 (1970)

    Article  ADS  Google Scholar 

  4. Symanzik, K. Small distance behaviour in field theory and power counting. Commun. Math. Phys. 18, 227–246 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  5. ‘t. Hooft, G. & Veltman, M. One-loop divergences in the theory of gravitation. Ann. Inst. Henri Poincaré A 20, 69–94 (1974)

    ADS  Google Scholar 

  6. Deser, S. & van Nieuwenhuizen, P. Nonrenormalizability of the quantized Einstein-Maxwell system. Phys. Rev. Lett. 32, 245–247 (1974)

    Article  ADS  Google Scholar 

  7. Deser, S. & van Nieuwenhuizen, P. One-loop divergences of quantized Einstein-Maxwell fields. Phys. Rev. D 10, 401–410 (1974)

    Article  ADS  Google Scholar 

  8. Deser, S. & van Nieuwenhuizen, P. Nonrenormalizability of the quantized Dirac-Einstein system. Phys. Rev. D 10, 411–420 (1974)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  9. Deser, S., Tsao, H. & van Nieuwenhuizen, P. One-loop divergences of the Einstein-Yang-Mills system. Phys. Rev. D 10, 3337–3342 (1974)

    Article  ADS  Google Scholar 

  10. Donoghue, J. F. Leading quantum correction to the Newtonian potential. Phys. Rev. Lett. 72, 2996–2999 (1994)

    Article  ADS  CAS  Google Scholar 

  11. Donoghue, J. F. General relativity as an effective field theory: the leading quantum corrections. Phys. Rev. D 50, 3874–3888 (1994)

    Article  ADS  CAS  Google Scholar 

  12. Burgess, C. P. Quantum gravity in everyday life: general relativity as an effective field theory. Living Rev. Relativity 〈http://www.livingreviews.org/lrr-2004-5〉 (2004)

  13. Robinson, S. P. & Wilczek, F. Gravitational correction to running of gauge couplings. Phys. Rev. Lett. 96, 231601 (2006)

    Article  ADS  Google Scholar 

  14. Gogoladze, I. & Cheung, C. N. Probing the gravitational scale via running gauge couplings. Phys. Lett. B 645, 451–454 (2007)

    Article  ADS  CAS  Google Scholar 

  15. Pietrykowski, A. R. Gauge dependence of gravitational correction to running of gauge couplings. Phys. Rev. Lett. 98, 061801 (2007)

    Article  ADS  Google Scholar 

  16. Vilkovisky, G. A. The unique effective action in quantum field theory. Nucl. Phys. B 234, 125–137 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  17. DeWitt, B. S. in Quantum Field Theory and Quantum Statistics Vol. 1 (eds Batalin, I. A., Isham, C. J. & Vilkovisky, G. A.) 191–222 (Hilger, 1987)

    Google Scholar 

  18. ‘t. Hooft, G. & Veltman, M. Regularization and renormalization of gauge fields. Nucl. Phys. B 44, 189–213 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  19. Toms, D. J. Quantum gravity and charge renormalization. Phys. Rev. D 76, 045015 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  20. Ebert, D., Plefka, J. & Rodigast, A. Absence of gravitational contributions to the running Yang-Mills coupling. Phys. Lett. B 660, 579–582 (2008)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. Tang, Y. & Wu, Y.-L. Gravitational contributions to the running of gauge couplings. Preprint at 〈http://arxiv.org/abs/0807.0331〉 (2008)

  22. Toms, D. J. Cosmological constant and quantum gravitational corrections to the running fine structure constant. Phys. Rev. Lett. 101, 131301 (2008)

    Article  ADS  Google Scholar 

  23. Toms, D. J. Quantum gravity, gauge coupling constants, and the cosmological constant. Phys. Rev. D 80, 064040 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  24. Ebert, D., Plefka, J. & Rodigast, A. Gravitational contributions to the running Yang-Mills coupling in large extra-dimensional brane worlds. J. High Energy Phys. 02, 028 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  25. Rodigast, A. & Schuster, T. Gravitational corrections to Yukawa and ϕ4 interactions. Phys. Rev. Lett. 104, 081301 (2010)

    Article  ADS  Google Scholar 

  26. Mackay, P. T. & Toms, D. J. Quantum gravity and scalar fields. Phys. Lett. B 684, 251–255 (2010)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  27. Daum, J.-E., Harst, U. & Reuter, M. Running gauge coupling in asymptotically safe quantum gravity. J. High Energy Phys. 01, 084 (2010)

    Article  ADS  Google Scholar 

  28. Shaposhnikov, M. & Wetterich, C. Asymptotic safety of gravity and the Higgs boson mass. Phys. Lett. B 683, 196–200 (2010)

    Article  ADS  CAS  Google Scholar 

  29. Zanusso, O., Zambelli, L., Vacca, G. P. & Percacci, R. Gravitational corrections to Yukawa systems. Phys. Lett. B 689, 90–94 (2010)

    Article  ADS  CAS  Google Scholar 

  30. Schwinger, J. S. On gauge invariance and vacuum polarization. Phys. Rev. 82, 664–679 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  31. DeWitt, B. S. The Dynamical Theory of Groups and Fields (Gordon and Breach, 1965)

    MATH  Google Scholar 

  32. Fradkin, E. S. & Tseytlin, A. A. On the new definition of off-shell effective action. Nucl. Phys. B 234, 509–523 (1984)

    Article  ADS  Google Scholar 

  33. Parker, L. E. & Toms, D. J. Quantum Field Theory in Curved Spacetime (Cambridge Univ. Press, 2009)

    Book  Google Scholar 

  34. Toms, D. J. Background-field method and the renormalization of non-Abelian gauge theories in curved space-time. Phys. Rev. D 27, 1803–1813 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  35. Gilkey, P. B. The spectral geometry of a Riemannian manifold. J. Diff. Geom. 10, 601–618 (1975)

    Article  MathSciNet  Google Scholar 

  36. Barvinsky, A. O. & Vilkovisky, G. A. The generalized Schwinger-DeWitt technique in gauge theories and quantum gravity. Phys. Rep. 119, 1–74 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  37. Toms, D. J. Renormalization of interacting scalar field theories in curved space-time. Phys. Rev. D 26, 2713–2729 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  38. Bunch, T. S. & Parker, L. Feynman propagator in curved spacetime: a momentum-space representation. Phys. Rev. D 20, 2499–2510 (1979)

    Article  ADS  Google Scholar 

  39. Peeters, K. Cadabra: a field-theory motivated symbolic computer algebra system. Comput. Phys. Commun. 176, 550–558 (2007)

    Article  ADS  CAS  Google Scholar 

  40. Spergel, D. N. et al. Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology. Astrophys. J. Suppl. Ser. 170, 377–408 (2007)

    Article  ADS  Google Scholar 

  41. Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. R. The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B 429, 263–272 (1998)

    Article  ADS  CAS  Google Scholar 

  42. Arkani-Hamed, N., Motl, L., Nicolis, A. & Vafa, C. The string landscape, black holes and gravity as the weakest force. J. High Energy Phys. 06, 060 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  43. Huang, Q. Gravitational correction and weak gravity conjecture. J. High Energy Phys. 03, 053 (2007)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK

    David J. Toms

Authors
  1. David J. Toms
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David J. Toms.

Ethics declarations

Competing interests

The author declares no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Toms, D. Quantum gravitational contributions to quantum electrodynamics. Nature 468, 56–59 (2010). https://doi.org/10.1038/nature09506

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature09506

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing