General Relativity and Gravitation

, Volume 16, Issue 7, pp 625–643 | Cite as

Scaling behavior of semiclassical gravity

  • Bruce L. Nelson
  • Prakash Panangaden
Research Articles


Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.


Stress Tensor Cosmological Constant Quantum Gravity Differential Geometry Scalar Quantum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nelson, B. L., and Panangaden, P. (1982).Phys. Rev. D,25, 1019.Google Scholar
  2. 2.
    Collins, J. C. (1976).Phys. Rev. D,14, 1965.Google Scholar
  3. 3.
    Brown, L. S., and Collins, J. C. (1980).Ann. Phys. (N. Y.),130, 215.Google Scholar
  4. 4.
    Parker, L. (1979). InRecent Developments in Gravitation, Cargese 1978, Levy, M., and Deser, S. eds. (Plenum, New York).Google Scholar
  5. 5.
    Bunch, T. S. (1979).J. Phys. A,14, 517.Google Scholar
  6. 6.
    Bunch, T. S., Panangaden, P., and Parker, L., (1980).J. Phys. A,13, 901; Bunch, T. S., and Panangaden, P. (1980).J. Phys. A,13, 919.Google Scholar
  7. 7.
    Bunch, T. S., and Parker, L. (1979).Phys. Rev. D,20, 2499.Google Scholar
  8. 8.
    Panangaden, P. (1980). Ph.D. thesis, University of Wisconsin-Milwaukee (unpublished).Google Scholar
  9. 9.
    Birrell, N. D., and Taylor, J. G. (1980).J. Math. Phys.,21, 1740; Birnell, N. C. (1980).J. Phys. A,13, 569.Google Scholar
  10. 10.
    Smolin, L. (1981). A fixed point for quantum gravity, Institute for Theoretical Physics (Santa Barbara, California), preprint, November 1981.Google Scholar
  11. 11.
    Weinberg, S. (1976). In Proceedings of the International School of Subnuclear Physics, Erice, Zichichi, A. ed,Google Scholar
  12. 12.
    Weinberg, S. (1973).Phys. Rev. D,8, 3497.Google Scholar
  13. 13.
    Collins, J. C., and Macfarlane, A. J. (1974).Phys. Rev. D,10, 1201.Google Scholar
  14. 14.
    Adler, S. L. (1982).Rev. Mod. Phys. 54, 729.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Bruce L. Nelson
    • 1
  • Prakash Panangaden
    • 1
  1. 1.Department of PhysicsUniversity of UtahSalt Lake City

Personalised recommendations