Classical Weyl-Spinor approach to U(1) and non-abelian local gauge theories

TL;DR

This paper develops a classical Weyl-spinor framework to describe fermions under U(1), SU(2), and SU(3) gauge fields, extending previous work to non-Abelian theories and potentially modeling early universe quark-gluon plasma.

Contribution

It introduces a covariant derivative along classical trajectories for fermions in non-Abelian gauge fields using a Weyl-spinor approach, expanding the classical gauge theory framework.

Findings

Derived classical spinor equations for non-Abelian gauge fields.

Extended covariant derivatives to SU(2) and SU(3) symmetries.

Potential application to quark-gluon plasma in early universe.

Abstract

In a previous paper we introduced two linear spinor equations equivalent to the Lorentz Force and stated that these equations were fairly general and could be applied to any force field compatible with Special Relativity. In this paper, via a lagrangian approach, we explore this possibility and obtain classical spinor equations describing the behaviour of fermionic particles not only under an electromagnetic field but also under Yang-Mills and Color fields. We find a covariant derivative defined {\it along the classical trajectory} of the particle, which can be extended to SU(2) and SU(3) local symmetries, and obtain the Yang-Mills and Color fields in a new classical Weyl-spinor approach to Gauge Theories. In the SU(3) case, the obtained equations which describe the behaviour of quarks under gluon fields could be in principle applied to the quark-gluon plasma phase existing during the first instants of the Universe.