Spacetime of the Elementary Particles

Abstract

The possibility is examined that physical space is characterized by a torsion, or an asymmetric connection, which is determined by the matter field. There exists a space with uniform torsion with the same metrical properties as conventional microspace; it is isotropic and homogeneous with a very large radius of curvature (R≅10²⁸ cm). The momentum operators form a group and for practical purposes commute. The torsion defines at every point two kinds of parallel transfer or two screw motions of opposite helicity. There are, consequently, two kinds of spinor field associated with the space; they are distinguished by opposite coupling to the torsion. Viewed from within the Lorentz group the torsion produces an axial vector interaction. To interpret the given mathematical model, it is suggested that there exists a universal axial vector coupling between fermions represented by the spinor fields and bosons associated with the torsion; and that this interaction manifests itself macroscopically as a torsion of space, in the same general way that gravitational interactions correspond to a curvature of space. This general assumption leads to cosmological models characterized by relations connecting the average density of matter and the strength of the assumed interaction. For the observed average density of matter in the known universe (∼10⁻³⁰ g/cm³) the proposed axial vector coupling turns out, for a space of uniform torsion, to be of the order of the strong interactions.