Gravitation and universal Fermi coupling in general relativity |
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Authors: | Hans-Jürgen Treder |
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Institution: | (1) Akademie der Wissenschaften, Potsdam-Babelsberg, German Democratic Republic |
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Abstract: | The generally covariant Lagrangian densityG = + 2K matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg
ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form
kl
i
=
kl
i
for the coefficients
kl
i
of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , gik, and the coefficients
kl
i
. Then the
kl
i
are determined by the Palatini equations. From these equations and from the symmetry
kl
i
=
lk
i
for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / 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 |
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Keywords: | |
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