Advertisement

On the Poincaré Gauge Theory of Gravitation

  • S. A. Ali
  • C. Cafaro
  • S. Capozziello
  • C. Corda
Article

Abstract

We present a compact, self-contained review of the conventional gauge theoretical approach to gravitation based on the local Poincaré group of symmetry transformations. The covariant field equations, Bianchi identities and conservation laws for angular momentum and energy-momentum are obtained.

Keywords

Gauge symmetry Riemann-Cartan geometry Gravity 

References

  1. 1.
    Utiyama, R.: Phys. Rev. 101, 1597 (1956) zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Yang, C.N., Mills, R.L.: Phys. Rev. 96, 191 (1954) CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Sciama, D.W.: On the analog between charge and spin in general relativity. In: Recent Developments in General Relativity, Festschrift for Leopold Infeld, p. 415. Pergamon Press, New York (1962) Google Scholar
  4. 4.
    Kibble, T.W.: Lorentz invariance and the gravitational field. J. Math. Phys. 2, 212 (1960) CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Grignani, G., et al.: Gravity and the Poincaré group. Phys. Rev. D 45, 2719 (1992) CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Hehl, F.W., et al.: Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rep. 258, 1–171 (1995) CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Inomata, A., et al.: General relativity as a limit of the de Sitter gauge theory. Phys. Rev. D 19, 1665 (1978) CrossRefADSGoogle Scholar
  8. 8.
    Ivanov, E.A., Niederle, J.: Gauge formulation of gravitation theories, I. The Poincaré, de Sitter and conformal cases. Phys. Rev. D 25, 976 (1982) CrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Ivanov, E.A., Niederle, J.: Gauge formulation of gravitation theories, II. The special conformal case. Phys. Rev. D 25, 988 (1982) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Mansouri, F., et al.: Gravity as a gauge theory. Phys. Rev. D 13, 3192 (1976) CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Mansouri, F.: Conformal gravity as a gauge theory. Phys. Rev. Lett. 42, 1021 (1979) CrossRefADSGoogle Scholar
  12. 12.
    Sardanashvily, G.: On the geometric foundation of classical gauge gravitation theory, arXiv:gr-qc/0201074
  13. 13.
    Chang, L.N., et al.: Geometrical approach to local gauge and supergauge invariance: Local gauge theories and supersymmetric strings. Phys. Rev. D 13, 235 (1976) CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Ne’eman, Y., Regge, T.: Gravity and supergravity as gauge theories on a group manifold. Phys. Lett. B 74, 54 (1978) CrossRefADSGoogle Scholar
  15. 15.
    Toller, M.: Classical field theory in the space of reference frames. Nuovo Cim. B 44, 67–98 (1978) CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Cognola, G., et al.: Theories of gravitation in the space of reference frames. Nuovo Cim. B 54, 325–348 (1979) CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Crawford, J.P.: Spinors in general relativity. In: Baylis, W.E. (ed.) Clifford (Geometric) Algebras: With Applications in Physics, Mathematics and Engineering. Birkhäuser, Basel (1996) Google Scholar
  18. 18.
    Hehl, F.W., et al.: General relativity with spin and torsion: foundations and prospects. Rev. Mod. Phys. 48, 393 (1976) CrossRefMathSciNetADSGoogle Scholar
  19. 19.
    Mansouri, F.: Superunified theories based on the geometry of local (super-) gauge invariance. Phys. Rev. D 16, 2456 (1977) CrossRefMathSciNetADSGoogle Scholar
  20. 20.
    Schouten, J.: Ricci Calculus. Springer, Berlin (1954) zbMATHGoogle Scholar
  21. 21.
    Dewitt, B.S.: Dynamical theory of groups and fields (Les Houches Lectures 1963). In: Relativity, Groups and Topology. Gordon and Breach, New York (1965) Google Scholar
  22. 22.
    Hehl, F.W., et al.: Nonlinear spinor equation and asymmetric connection in general relativity. J. Math. Phys. 12, 1334 (1970) CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    Blagojevic, M.: Three lectures on Poincaré gauge theory, arXiv:gr-qc/0302040
  24. 24.
    Wald, R.M.: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. The University of Chicago Press, Chicago (1994) zbMATHGoogle Scholar
  25. 25.
    Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982) zbMATHGoogle Scholar
  26. 26.
    Carroll, S., et al.: Consequences of propagating torsion in connection dynamic theories of gravity, arXiv:gr-qc/9403058
  27. 27.
    Shapiro, I.L.: Physical aspects of spacetime torsion, arXiv:hep-th/0103093
  28. 28.
    Brill, D.R., et al.: Interaction of neutrinos and gravitational fields. Rev. Mod. Phys. 29, 465 (1957) zbMATHCrossRefMathSciNetADSGoogle Scholar
  29. 29.
    Schwinger, J.: Energy and momentum density in field theory. Phys. Rev. 130 (1962) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • S. A. Ali
    • 1
  • C. Cafaro
    • 2
  • S. Capozziello
    • 3
  • C. Corda
    • 4
  1. 1.Department of PhysicsState University of New York at Albany-SUNYAlbanyUSA
  2. 2.Dipartimento di FisicaUniversità di CamerinoCamerinoItaly
  3. 3.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II” and INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio GNapoliItaly
  4. 4.Associazione Scientifica Galileo GalileiPratoItaly

Personalised recommendations