Theoretical and Mathematical Physics

, Volume 140, Issue 2, pp 1095–1108 | Cite as

Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature

  • Yu. V. Pavlov

Abstract

We consider a scalar field with a Gauss–Bonnet-type coupling to the curvature in a curved space–time. For such a quadratic coupling to the curvature, the metric energy–momentum tensor does not contain derivatives of the metric of orders greater than two. We obtain the metric energy–momentum tensor and find the geometric structure of the first three counterterms to the vacuum averages of the energy–momentum tensors for an arbitrary background metric of an N-dimensional space–time. In a homogeneous isotropic space, we obtain the first three counterterms of the n-wave procedure, which allow calculating the renormalized values of the vacuum averages of the energy–momentum tensors in the dimensions N = 4, 5. Using dimensional regularization, we establish that the geometric structures of the counterterms in the n-wave procedure coincide with those in the effective action method.

scalar field quantum theory in curved space renormalization dimensional regularization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    A. A. Grib, S. G. Mamayev, and V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields, Friedmann Laboratory Publ., St. Petersburg (1994).Google Scholar
  2. 2.
    N. D. Birell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Univ. Press, Cambridge (1982).Google Scholar
  3. 3.
    A. A. Grib and E. A. Poberii, Helv. Phys. Acta., 68, 380 (1995); X. S. Mamaeva and N. N. Trunov, Theor. Math. Phys., 135, 520 (2003).Google Scholar
  4. 4.
    A. D. Linde, Physics of Elementary Particles and Inflation Cosmology [in Russian], Nauka, Moscow (1990).Google Scholar
  5. 5.
    M. Bordag, J. Lindig, V. M. Mostepanenko, and Yu. V. Pavlov, Internat. J. Mod. Phys. D, 6, 449 (1997); V. B. Bezerra, V. M. Mostepanenko, and C. Romero, Modern Phys. Lett. A, 12, 145 (1997); S. Habib, C. Molina-París, and E. Mottola, Phys. Rev. D, 61, 024010 (2000).CrossRefGoogle Scholar
  6. 6.
    R. M. Wald, Comm. Math. Phys., 54, 1 (1977).Google Scholar
  7. 7.
    D. Lovelock, J. Math. Phys., 12, 498 (1971).CrossRefGoogle Scholar
  8. 8.
    B. Zwiebach, Phys. Lett. B, 156, 315 (1985).CrossRefGoogle Scholar
  9. 9.
    S. V. Ketov, Introduction to the Quantum Theory of Strings and Superstrings [in Russian], Nauka, Novosibirsk (1990).Google Scholar
  10. 10.
    Ya. B. Zel'dovich and A. A. Starobinsky, JETP, 34, 1159 (1972).Google Scholar
  11. 11.
    C. Lanczos, Ann. Math., 39, 842 (1938).Google Scholar
  12. 12.
    H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrö dinger Operators with Applications to Quantum Mechanics and Global Geometry, Springer, Berlin (1987).Google Scholar
  13. 13.
    T. S. Bunch, J. Phys. A, 12, 517 (1979).Google Scholar
  14. 14.
    S. A. Fulling, Aspects of Quantum Theory in Curved Space-Time, Cambridge Univ. Press, Cambridge (1991).Google Scholar
  15. 15.
    G.'t Hooft, Nucl. Phys. B, 61, 455 (1973).CrossRefGoogle Scholar
  16. 16.
    Yu. V. Pavlov, Internat. J. Mod. Phys. A, 17, 1041 (2002).CrossRefGoogle Scholar
  17. 17.
    Yu. V. Pavlov, Theor. Math. Phys., 138, 383 (2004).CrossRefGoogle Scholar
  18. 18.
    S. G. Mamayev, V. M. Mostepanenko, and V. A. Shelyuto, Theor. Math. Phys., 63, 366 (1985).Google Scholar
  19. 19.
    S. Mignemi and N. R. Stewart, Phys. Rev. D, 47, 5259 (1993).CrossRefGoogle Scholar
  20. 20.
    E. W. Mielke and F. E. Schunck, Nucl. Phys. B, 564, 185 (2000). 1108CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Yu. V. Pavlov
    • 1
  1. 1.Institute of Mechanical Engineering and Friedmann Laboratory for Theoretical PhysicsSt. PetersburgRussia

Personalised recommendations