Yang Mills model of interacting particles in the classical field theory

TL;DR

This paper explores a classical field theory model for interacting particles within General Relativity, using Clifford algebra and connections on principal bundles, addressing symmetries and the Higgs mechanism.

Contribution

It introduces a Yang-Mills type model for particles in classical field theory, incorporating Clifford algebra and gauge connections, with detailed analysis of symmetries and scalar products.

Findings

Found a solution for individual particles in the model

Analyzed symmetry problems including the Higgs mechanism

Developed a pedagogical framework for classical particle interactions

Abstract

The purpose is to study systems of interacting particles in the Generl Relativity context, by the principle of least action using purely classical concepts. The particles are described by a state tensor using a Clifford algebra for the kinematic part. The force fields, including gravitation, are described by connections on principle bundles. A solution has been found to account for individual particles. A more specific model based on scalar products, Dirac operator and chirality is studied in more details. Problems related to symmetries, including the Higgs mechanism, are intoduced. With a comprehensive coverage of topics it can be a useful pedagogical study.