Narrow Results

We propose a spinorial approach to the unified electroweak interactions, in which no use is made of spontaneous symmetry breakdown. No scalar particles are needed in order to break the symmetry. No reference is made to gauge symmetry. Our approach stresses the role of space–time and isospin symmetries in the build up of the electroweak model. Internal degrees of freedom, such as isospin, are incorporated in the theory by using spinors carrying isospin indices. All vector bosons are described by a rank 2 field in the spinorial and the isospinorial indices. Leptons are accomodated in a rank 1 spinor field and in a rank 2 isospin field as well. The dynamical variables of the theory are the chiral and isochiral components of these fields.

By ascribing a complex anticommuting variable ζ to each basic property of a field it is possible to describe all the fundamental particles as combinations of only five ζ and understand the occurrence of particle generations. An extension of space-time x to include property then specifies the 'where, when and what' of an event and allows for a generalized relativity where the gauge fields lie in the x - ζ sector and the Higgs fields in the ζ - ζ sector.

We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute or property, to space–time location. (With five such properties one can accommodate all known leptons and quarks.) Using just one property, viz. electricity, the general relativity of such a scheme and its superscalar curvature automatically produces the Einstein–Maxwell Lagrangian and a cosmological term. By adding more properties we envisage the geometrical unification of the standard model with gravitation.

By ascribing a complex anticommuting variable ζ to each basic property of a field it is possible to describe all the fundamental particles as combinations of only five ζ and understand the occurrence of particle generations. An extension of space-time x to include property then specifies the 'where, when and what' of an event and allows for a generalized relativity where the gauge fields lie in the x – ζ sector and the Higgs fields in the ζ – ζ sector.

We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute or property, to space–time location. (With five such properties one can accommodate all known leptons and quarks.) Using just one property, viz. electricity, the general relativity of such a scheme and its superscalar curvature automatically produces the Einstein–Maxwell Lagrangian and a cosmological term. By adding more properties we envisage the geometrical unification of the standard model with gravitation.