Foundations of Physics

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

Gravitation and universal Fermi coupling in general relativity

  • Hans-Jürgen Treder


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


General Relativity Wave Equation Coupling Factor Matter Field Spinor Field 
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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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