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Foundations of Physics

, Volume 6, Issue 5, pp 527–538 | Cite as

Gravitation and universal Fermi coupling in general relativity

  • Hans-Jürgen Treder
Article

Abstract

The generally covariant Lagrangian densityG = ℛ + 2Kmatter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsgikand φ of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form Γ kl i = kl i for the coefficients г kl i of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of φ, gik, and the coefficients г kl i . Then the г kl i are determined by the Palatini equations. From these equations and from the symmetry г kl i = г lk i for all matter fields with δℒ/δΓ=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, δℒ/δΓ becomes dependent on the Dirac current, essentially with a coupling factor ∼Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10−81erg cm3

Keywords

General Relativity Wave Equation Coupling Factor Matter Field Spinor Field 
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.

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References

  1. 1.
    A. Einstein,Sitzungsber. Akad. Wiss. (Berlin), Phys.-Math. Kl. 1925, 414.Google Scholar
  2. 2.
    A. Einstein,The Meaning of Relativity (Princeton, University Press, 1950), Appendix II.Google Scholar
  3. 3.
    H. Weyl,Z. Phys. 56, 330 (1929).Google Scholar
  4. 4.
    H. Weyl,Phys. Rev. 77, 699 (1950).Google Scholar
  5. 5.
    W. Heisenberg,Einführung in die einheitliche Feldtheorie der Elementarteilchen (Hirzel, Stuttgart, 1967).Google Scholar
  6. 6.
    W. Heisenberg,Naturwiss. 61, 1 (1974).Google Scholar
  7. 7.
    H.-J. Treder,Acta Phys. Hung. 32, 49 (1972).Google Scholar
  8. 8.
    A. Einstein,Sitzungsber. Akad. Wiss. (Berlin), Phys.-Math. Kl. 1923, 137.Google Scholar
  9. 9.
    H. Weyl,Naturwiss. 38 (1950).Google Scholar
  10. 10.
    A. Palatini,Rend. Circ. Mat. Palermo 43, 203 (1919).Google Scholar
  11. 11.
    W. Pauli,Theory of Relativity (Pergamon Press, Oxford, 1958).Google Scholar
  12. 12.
    L. Infeld and B. L. van der Waerden,Sitzungsber. Akad. Wiss. (Berlin), Phys.-Math. Kl. 1933, No. IX.Google Scholar
  13. 13.
    H.-J. Treder,Ann. Phys. (Leipzig) 32, 238 (1975).Google Scholar
  14. 14.
    J. J. Sakurai,Invariance Principles and Elementary Particles (Princeton University Press, Princeton, New Jersey, 1964).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Hans-Jürgen Treder
    • 1
  1. 1.Akademie der WissenschaftenPotsdam-BabelsbergGerman Democratic Republic

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