Eight-dimensional unified theory

Mathematics

Scientific paper

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Electromagnetic Fields, Field Theory (Physics), Gravitation Theory, Manifolds (Mathematics), Particle Interactions, Space-Time Functions, Leptons, Spinor Groups, Tensors

Scientific paper

Some foundations are laid for a unified theory of weak, electromagnetic, and gravitational interactions within a framework of an 8-dimensional metrical manifold with one timelike and seven spacelike dimensions, four of them being tightly closed and forming a subspace of unitary spin. All eight dimensions are equivalent locally so that the theory should be generally covariant under infinitesimal transformations, but four of them are sharply distinguished topologically, which constitutes a reason for some symmetry breaking. The scalar curvature of the 8-dimensional manifold R(8) is assumed as a Lagrangian for the theory, and by splitting the metric tensor according to Salam (1968), the Lagrangian may be shown to split into the usual Einsteinian R(4). A 16-component spinor is formed by introducing a heavy neutrino and regarding the positively charged muon and the right-handed muonic neutrino as leptons. It appears that color will be accountable under this scheme.

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