Scalar fields in a seven-dimensional manifold behaving as Lorentz- covariant spinor fields in space-time (Q1179152)

The author presents a Lorentz-invariant model of the physical vacuum based on a 7-dimensional manifold with the topology \(M^ 4\otimes S^ 3\) (where \(M^ 4\) is Minkowski space and \(S^ 3\) is a 3-dimensional sphere) and endowed with a statistical metric tensor. It is shown that certain scalar fields on such a manifold behave like spinor fields when viewed from their space-time projection. The results extend the author's previous work [Gen. Relativ. Gravitation 19, 295-322 (1987; Zbl 0605.53038); Phys. Rev. D 38, 3710-3714 (1988)] from \(SO(3)\)-covariance to Lorentz-covariance and are intended to provide clues for the construction of theories unifying gravity with other interactions. Contents include: an introduction (which provides a survey of his previous work); a 7- dimensional Riemannian manifold as a model for the physical vacuum; complex formulation of a real manifold; Lorentz invariance of our vacuum model; scalar fields behaving as Lorentz spinors, and appendices containing proofs, and a discussion of classical models of quantization.