Advertisement

Gauge Theories of Gravitation

  • W. Thirring
Part of the Acta Physica Austriaca book series (FEWBODY, volume 19/1978)

Abstract

The theories of electromagnetism and gravitation are the best understood classical field theories. The former serves as model for gauge theories which are conjectured to describe weak and strong interactions. It is therefore natural to ask whether Einstein’s theory (G.R.) of gravitation is such a gauge theory. In G.R. one considers the metric g as the analogue to the potential A and the connection ω (the generalized Christoffel symbols) as the analogue to the field strength F. This is not what formally appears in a gauge theory of gravitation where ω corresponds to the potential and the curvature R to the field strength:

Keywords

Gauge Theory Fibre Bundle Gauge Field Exterior Derivative Cosmological Term 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Thirring, Lehrbuch der Mathematischen Physik, Bd.1, Springer 1977, Bd. 2, Springer 1978.Google Scholar
  2. Y. Choquet-Bruhat, C. DeWitt-Morette, M.Dillard-Bleick: Analysis, Manifolds and Physics, North Holland 1978.Google Scholar
  3. C. Misner, K. Thorne, J. Wheeler, Gravitation, Freeman 1973.Google Scholar
  4. 2.
    J. Dieudonné, Foundations of Modern Analysis (X,9), Academic Press, 1960.Google Scholar
  5. 3.
    A. Trautman, Reports on Mathematical Physics 1 (1970) 29. M. Mayer, Lecture Notes in Mathematics, 570, Springer 1976MathSciNetGoogle Scholar
  6. 4.
    C.N. Yang, “Integral Formalism for Gauge Fields”, Phys. Rev. Lett. 33 (1974) 445.MathSciNetADSCrossRefGoogle Scholar
  7. C.N. Yang, “Gauge Fields”, Proceedings of the Sixth Hawaii Topical Conference in Particle Physics (1975), Ed. by P.N. Dobson, Jr., S. Pakvasa, V.Z. Peterson and S.F. Tuan, p. 489, University of Hawaii at Manoa, Honolulu.Google Scholar
  8. Ni Wei-Tou, “Yang’s Gravitational Field Equations,”Phys. Rev. Lett. 35 (1975) 319.Google Scholar
  9. A.H. Thompson, “Geometrically Degenerate Solutions of the Kilmister-Yang Equations”, Phys. Rev. Lett. 35 (1975) 320.MathSciNetADSCrossRefGoogle Scholar
  10. R. Pavelle, “Unphysical Solutions of Yang’s Gravitational Field Equations,”Phys. Rev. Lett. 34 (1975) 1114.Google Scholar
  11. R. Pavelle, “Unphysical Characteristics of Yang’s Pure-Space Equations”, Phys. Rev. Lett. 37 (1976) 961.ADSCrossRefGoogle Scholar
  12. R. Pavelle, “Mansouri-Chang Gravitation Theory” Phys. Rev. Lett. 40 (1976) 267.MathSciNetADSCrossRefGoogle Scholar
  13. Y.M. Cho, “Einstein Lagrangian as the Translational Yang-Mills Lagrangian,”Phys. Rev. D14 (1976) 2521.Google Scholar
  14. Y.M. Cho, “Gauge Theory of Poincaré Symmetry,”Phys. Rev. D14 (1976) 3335.CrossRefGoogle Scholar
  15. M. Camenzind, “On the Curvature Dynamics for Metric Gravitational Theories,”J. Math. Phys. 16 (1974) 1023.Google Scholar
  16. M. Camenzind, “On the Yang-Mills Structure of Gravitation: A New Issue of the Final State”, GRG 8 (1977) 103.MathSciNetGoogle Scholar
  17. M. Camenzind, “The Gravitational Field of Spherically Symmetric Matter Distributions in the Yang-Mills Gauge Theory of Gravity”, Phys. Lett. 63A (1977) 69.MathSciNetADSGoogle Scholar
  18. M. Camenzind, Phys. Rev. D16 (1977) Nr. 12.Google Scholar
  19. M. Camenzind, “The Fundamental Modes of Gravity”, to be published.Google Scholar
  20. M. Camenzind, “Lepton Pair Creation and the Uniform Gravitational Collapse”, to be published.Google Scholar
  21. E.E. Fairchild, Jr., “Yang-Mills Formulation of Gravitational Dynamics”, Phys. Rev. D16 (1977) 2438.Google Scholar
  22. T.T. Wu, C.N. Yang, “Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields”, Phys. Rev. D12 (1975) 3845.MathSciNetADSCrossRefGoogle Scholar
  23. 5.
    P. Havas, GRG 8 (1977) 631.Google Scholar
  24. 6.
    Y. Cho, Phys. Rev. D14 (1976) 2521.Google Scholar
  25. 7.
    S. Mac Dowell, R. Mansouri, Phys. Rev. Lett. 38, (1977) 739.Google Scholar
  26. Compare E. Drechsler, Lecture Notes in Mathematics 570, Springer 1976.Google Scholar
  27. 8.
    Sitzber. Preuss. Akad. Wiss. 966 (1921).Google Scholar
  28. 9.
    O. Klein, Z. Physik 37, 895 (1926).Google Scholar
  29. R. Kerner, Ann. Inst. H. Poincaré 9 (1968) 143.Google Scholar
  30. Y. Cho, J. Math. Phys. 16 (1975) 2029.Google Scholar
  31. W. Thirring, Acta Phys. Austr. Suppl. IX, (1972) 256. J. Rayski, Acta Phys. Polon. 27 (1965) 89.Google Scholar
  32. 10.
    Z. Horvath, L. Palla, E. Cremmer, J. Scherk, Nucl. Phys. B127 (1977) 57.Google Scholar
  33. 11.
    H. Narnhofer, W. Thirring, The taming of the dipole ghost, Vienna preprint 1978.Google Scholar
  34. 12.
    W. Thirring, R. Wallner, Use of differential forms in General Relativity, Vienna preprint 1978.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • W. Thirring
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienAustria

Personalised recommendations