A vector model for electroweak interactions

Abstract

In this paper we present a vector model for the electroweak interactions. The Cartan map gives an isomorphism between Dirac bispinors and an isotropic class of Yang–Mills vector fields. The isotropic Yang–Mills vector fields Fk =Ek +iHk with k=1,2,3, satisfy the condition that the matrix of scalar invariants (Fj ⋅Fk) equals a scalar multiple of the identity matrix. We show that all the bispinor observables commute with the Cartan isomorphism, including all gauge transformations, as well as Lorentz transformations. We derive the Yang–Mills equivalent Dirac equation. As a consequence of the vector model, we obtain a new Lagrangian for electroweak interactions, which is an alternative to the Weinberg–Salam Lagrangian. Moreover, we show that the vector model predicts that the Weinberg angle θw satisfies sin2 θw =0.25, which is close to the measured value of sin2 θw =0.23. The vector model accommodates all the lepton and quark flavors. Furthermore, it predicts the conservation of baryon number and lepton number, as well as electric charge in electroweak interactions. The vector model also gives a new interpretation to antiparticles. In the vector model, an antiparticle is characterized by its opposite baryon number, lepton number, and electric charge; yet both particles and antiparticles propagate forward in time with positive energies.