New Geometric Framework for SU(2) Gauge Theory

TL;DR

This paper introduces a geometric framework for SU(2) gauge theory using fiber bundles with local vector space fibers, deriving gauge connections and equations that reduce solution ambiguities and reveal new solutions for specific field configurations.

Contribution

It presents a novel geometric model for SU(2) gauge theory with a reduced solution space and explicit equations derived from local isotopic frames.

Findings

Yang-Mills equations are derived from the new framework.

The solution space is highly constrained, eliminating certain ambiguities.

New solutions for punctual source and spherical wave fields are found.

Abstract

An explicit model of fiber bundle with local fibers being disinct copies of vector 3-space is introduced. They are endowed with frames which are used as local isotopic ones. The field local of isotopic frames is considered as gauge field itself while the form of gauge connections is derived from it. A covariant equation for the field of local frames is found. It is shown that Yang-Mills equation follows from it, but variety of solutions of the new equation is highly reduced in such that no ambiguities (Yang-Wu and vacuum ones) arise. It is shown that Lagrangian for the field gives non-zero trace for the stress-energy tensor and zero value for spin of the field of plane wave. Some new solutions for the fields of punctual source and spherical wave are found.