Model of the electro-weak, gravitational and strong interactions in the   O-theory
  Based on the matrix representation of octonion algebra, supplied with specific multiplication rule, the model of electroweak and gravitational interactions is built up. While electroweak interaction in this model is induced by charged W-bosons, other two forces appear to have slightly more complicated nature. Gravitational interaction coincides in the model with dipole interaction of a pair of charged bosons. The dipole consists of a charged vector bosons pair from the major octonion algebra fields. When the charged dipole pair interacts with the neutral bosons pair from the major octonion algebra fields, the charged bosons pair misses its mass. The drop in mass leads to appearance of far-ranging forces of gravitational interaction. Finally, strong interaction appears in the model as internal gravitational solution of 'black whole' type with the peculiar 'gravitational' constant. The solution is a product of interaction of major vector fields pair with charged W-bosons pair. It is inferred from the model that the state space is ten-dimensional. The space is built as a module of the matrix representation of octonion algebra over the particles field (O-module). Similarly to the Standard Weinberg-Salam theory, the particle mass here appears as the product of interaction of massless spinor fields and Higgs field from O-module representation. 
V. Yu. Dorofeev
gr-qc nucl-th