Yang Mills model of interacting particles in the classical field theory

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.