Other
Scientific paper
Feb 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979gregr..10..231h&link_type=abstract
General Relativity and Gravitation, Volume 10, Issue 3, pp.231-252
Other
Scientific paper
A nonlocal spinor field theory of electromagnetically neutral matter is developed in which both gravitational field and its source emerge from a quadrilocal extension of the complex Weyl spinor, the sources finding expression in terms of the local limit of the derivatives with respect to the internal coordinates of that part of the nonlocal field that indeed vanishes locally. The structure of the nonlocal field is dictated by its field equations, which are obtained using a prescription suggested by a manifestly covariant reformulation of the field equations derived by Fröhlich for a bilocal extension of the complex Maxwell spinor. As in the electrodynamic case the additional (complex) components (three in the gravitational case) act as potentials for the matter current, which is identified through the identity of the inhomogeneous field equations obtained for the field intensities with the form assumed by the Bianchi identities when matter is introduced via the Einstein equations. The conservation of source is shown to follow directly from the initial homogeneous, nonlocal field equations, and in the weak-field, nonrelativistic limit a simple expression, in terms of the nonlocal field, is obtained for the mass density associated with the matter source. A satisfactory derivation of the Lorentz equation of motion for charged sources, on the other hand, is still lacking, pending a synthesis of the Maxwell and Weyl fields, some remarks on wich, together with a speculation concerning the quantization of the bilocal Maxwell field, conclude the work.
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