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

TL;DR

This paper proposes a unified framework for modeling elementary particles and their interactions without relying on gauge symmetry, introducing three models that replicate aspects of electroweak and strong interactions.

Contribution

It introduces a novel approach to particle modeling that avoids gauge symmetry, providing new models with fixed parameters and insights into particle interactions.

Findings

First model reproduces part of GWS interactions but has a flaw.

Second model fixes the flaw and predicts a specific Weinberg angle.

Third model suggests a connection between spinor configurations and color charge.

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.