General Relativity and Gravitation

, Volume 4, Issue 1, pp 1–11 | Cite as

Minimal and nonminimal gravitational interactions, and the asymmetric energy momentum tensor

  • Kenji Hayashi
Research Articles


Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b k μ, which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincaré gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.


General Relativity Physical Meaning General Framework Differential Geometry Gauge Transformation 
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  1. 1.
    Weyl, H. (1929).Z. Phys.,56, 330; Fock, V. (1929).Z. Phys.,57, 261.Google Scholar
  2. 2.
    Hayashi, K. and Nakano, T. (1967).Prog. Theor. Phys.,38, 491.Google Scholar
  3. 3.
    Schrodinger, E. (1954).Spaae-Time Structure, (Cambridge University Press).Google Scholar
  4. 4.
    Hayashi, K. (1968).Prog. Theor. Phys.,39, 494.Google Scholar
  5. 5.
    Belinfante, F.J. (1940).Physica,7, 449.Google Scholar
  6. 6.
    Miyamoto, S. and Nakano, T. (1971).Prog. Theor. Phys.,45, 295.Google Scholar
  7. 7.
    Pound, R.V. and Snider, J.L. (1965).Phys. Rev.,B140, 788.Google Scholar
  8. 8.
    Thorne, K.S. and Will, C.M. (1971).Astrophys. J.,163, 595.Google Scholar
  9. 9.
    Pauli, W. (1958).Theory of Relativity, (Pergamon Press, Oxford).Google Scholar
  10. 10.
    For a detailed discussion of this infinite Lorentz gauge group and gravitation, see Hayashi, K. and Bregman, A. (1972). “Poincaré Gauge Invariance and the Dynamical Role of Spin in Gravitational Theory”,Ann. Phys. (N.Y.),74, (December issue), (to appear).Google Scholar

Copyright information

© Plenum Publishing Company Limited 1973

Authors and Affiliations

  • Kenji Hayashi
    • 1
  1. 1.Max Planck-Institut für Physik und AstrophysikMünchen

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