Gravitation and Electrodynamics over SO(3,3)


In a series of papers, an approach to field theory is developed in which matter appears by interpreting source-free (homogeneous) fields over a 6-dimensional space of signature (3,3), as interacting (inhomogeneous) fields in space-time. The extra dimensions are given a physical meaning as “coordinatized matter.” The inhomogeneous energy-momentum relations for the interacting fields in space-time are automatically generated by the simple homogeneous relations in 6-d. We then develop a Weyl geometry over SO(3,3) as base, under which gravity and electromagnetism are essentially unified via an irreducible 6-calibration invariant Lagrange density and corresponding variational principle. The Einstein–Maxwell equations are shown to represent a low-order approximation, and the cosmological constant must vanish in order that this limit exist.

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  1. Weinberg, S. (1972). Gravitation and Cosmology, Wiley, p. 7.1, p. 10.8.

  2. Weyl, H. (1917). Annalen der Physik, 54, 121-125, 133

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  3. Weyl, H. (1918). Sitzungsb. Akad. der Wiss. Berlin, 465-480.

  4. Weyl, H. (1952). Space-Time-Matter, Dover, reprint, sec. 35, New York.

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Lunsford, D.R. Gravitation and Electrodynamics over SO(3,3). International Journal of Theoretical Physics 43, 161–177 (2004).

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  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Physical Meaning
  • Variational Principle