Models for elementary particles under a unified framework without making use of gauge symmetry

Abstract

This paper consists of two parts. In the first part, a concise reformulation is derived for that part of the Glashow-Weinberg-Salam (GWS) electroweak interaction Hamiltonian, which describes interactions between leptons (in the first generation) and vector bosons. In this reformulation, different particle species are associated with different types of spinor spaces for the description of their spin states and, as a consequence, the former are characterizable by configurations of the latter. In the second part, based on results of the first part, a framework is proposed which may be useful for constructing models of elementary particles and their interactions without making use of gauge symmetry at the fundamental level. Three models within this framework are constructed and studied. The first model predicts the above mentioned part of the GWS electroweak interactions, while, it suffers a flaw. Remove of the flaw by a small modification gives rise to a second model; and, as a byproduct of the modification, this model contains only one coupling constant, with the Weinberg angle fixed at $\sin^2 \theta_{W} = 0.25$. The third model predicts interactions that show certain similarities to strong interactions, with the quantum number of color related to certain type of spinor-space configuration.