Advertisement

Foundations of Physics

, Volume 41, Issue 2, pp 270–277 | Cite as

BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity

  • Mir FaizalEmail author
Article

Abstract

In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.

Keywords

BRST Anti-BRST Perturbative quantum gravity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972) Google Scholar
  2. 2.
    Becchi, C., Rouet, A., Stora, R.: Ann. Phys. 98, 287 (1976) CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Ojima, I.: Prog. Theor. Phys. 64, 625 (1980) zbMATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Nakanishi, N.: Prog. Theor. Phys. 59, 972 (1978) zbMATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Kugo, T., Ojima, I.: Nucl. Phys. B 144, 234 (1978) CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Nishijima, K., Okawa, M.: Prog. Theor. Phys. 60, 272 (1978) zbMATHCrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Nakanishi, N., Ojima, I.: Covariant Operator Formalism of Gauge Theories and Quantum Gravity, World Sci. Lect. Notes. Phys. World Scientific, Singapore (1990) Google Scholar
  8. 8.
    Kitazawa, Y., Kuriki, R., Shigura, K.: Mod. Phys. Lett. A 12, 1871 (1997) zbMATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Benedict, E., Jackiw, R., Lee, H.J.: Phys. Rev. D 54, 6213 (1996) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Brandt, F., Troost, W., Van Proeyen, A.: Nucl. Phys. B 464, 353 (1996) zbMATHCrossRefADSGoogle Scholar
  11. 11.
    Tahiri, M.: Int. J. Theor. Phys. 35, 1572 (1996) CrossRefMathSciNetGoogle Scholar
  12. 12.
    Menaa, M., Tahiri, M.: Phys. Rev. D 57, 7312 (1998) CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Ghiotti, M., Kalloniatis, A.C., Williams, A.G.: Phys. Lett. B 628, 176 (2005) CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    von Smekal, L., Ghiotti, M., Williams, A.G.: Phys. Rev. D 78, 085016 (2008) CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Curci, G., Ferrari, R.: Phys. Lett. B 63, 91 (1976) CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Hawking, S.W., Hayward, J.D.: Phys. Rev. D 49, 5252 (1994) CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems. Princeton University Press, Princeton (1992) zbMATHGoogle Scholar
  18. 18.
    Mieg, J.T.: J. Math. Phys. 21, 2834 (1980) CrossRefMathSciNetADSGoogle Scholar
  19. 19.
    Higuchi, A., Spyros, S.K.: Class. Quantum Gravity 18, 4317 (2001) zbMATHCrossRefADSGoogle Scholar
  20. 20.
    Kondo, K.I., Shinohara, T.: Phys. Lett. B 491, 263 (2000) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsDurham UniversityDurhamUK

Personalised recommendations