Contracted Bianchi Identities and Conservation Laws in Poincaré Gauge Theories of Gravity

  • Wiktor Szczyrba
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 58)

Abstract

For Poincaré gauge theories of gravity we derive differential identities of the Belinfante-Rosenfeld and of the Bianchi type. We construct two conserved Noether 3-forms which are related to energy -momentum and angular momentum, respectively.

Keywords

Gauge Theory Field Equation BIANCHI Identity Tensor Field Matter Field 
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References

  1. 1.
    R.Adler, M.Bazin and M.Schiffer, Introduction to general relativity, McGraw Hill, New York (1965).MATHGoogle Scholar
  2. 2.
    R.Arnowitt, S.Deser and C.W.Misner, The dynamics of general relativity, in: Gravitation-an introduction to current research, L.Witten, ed., John Wiley, New York (1962).Google Scholar
  3. 3.
    E.Fairchild,Jr., Phys.Rev 14D:384 (1976) and Phys.Rev. 16D: 2438 (1977).MathSciNetADSGoogle Scholar
  4. 4.
    A.Fischer and J.Marsden, GRG 7: 915 (1976).MathSciNetMATHGoogle Scholar
  5. 5.
    A.Fischer and J.Marsden, The initial value problem and the dynamical formulation of general relativity, in: General relativity. An Einstein centenary survey, S.Hawking and W.Israel eds. Cambridge University Press (1979).Google Scholar
  6. 6.
    H.Goldschmidt and S.Sternberg, Ann.Inst.Fourier (Grenoble) 23: 203 (1973).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    F.Hehl, P. von der Heyde, G.Kerlick and J.Nester, Rev.Mod.Phys. 48:: 393 (1976).ADSCrossRefGoogle Scholar
  8. 8.
    F.Hehl, Y.Ne’eman, J.Nitsch and P. von der Heyde, Phys.Lett. 78B:: 102 (1978).ADSGoogle Scholar
  9. 9.
    F.Hehl, J.Nitsch and P.von der Heyde, Gravitation and Poincare gauge field theory with quadratic lagrangian, in: Einstein Volume, Plenum Press (to appear 1979 ).Google Scholar
  10. 10.
    P. von der Heyde, Phys.Lett. 58A: 141 (1976).MathSciNetCrossRefGoogle Scholar
  11. 11.
    J.Kijowski, Comm.Math.Phys. 30: 99 (1973).MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    J.Kijowski, GRG 9: 857 (1978).MathSciNetMATHGoogle Scholar
  13. 13.
    A.Komar, Phys. Rev. 113: 934 (1959).MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    F.Mansouri and L.N.Chang, Phys.Rev. 13D: 3192 (1976).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    C.Misner, K.Thorne and J.Wheeler, Gravitation, W.H.Freeman, San Francisco (1973).Google Scholar
  16. 16.
    Y.Ne’eman and T.Regge, Rivista del Nuovo Cimento l,n5 (1978).Google Scholar
  17. 17.
    J.A.Schouten, Ricci Calculus, Springer, Berlin-Heidelberg-N.Y (1954)MATHGoogle Scholar
  18. 18.
    W.Szczyrba, Comm.Math.Phys. 51: 163 (1976).MathSciNetADSMATHCrossRefGoogle Scholar
  19. 19.
    W.Szczyrba, Lett.Math.Phys. 2: 265 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    W.Szczyrba, Comm.Math.Phys. 60: 215 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    W.Szczyrba, A hamiltonian structure of the interacting gravitational and matter fields (preprint 1978).Google Scholar
  22. 22.
    A.Trautman, Symposia Math. 12: 139 (1973).MathSciNetGoogle Scholar
  23. 23.
    A.Trautman, Elementary introduction to fibre bundles and gauge fields, Warsaw University - preprint (1978).Google Scholar
  24. 24.
    C.N.Yang, Phys.Rev.Lett. 33: 445 (1974).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Wiktor Szczyrba
    • 1
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of CologneCologneGermany
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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