A Self-Dual Model for the SU(2) Gauge Theory

TL;DR

This paper constructs a gauge-invariant model of SU(2) gauge theory on a specific space-time, deriving metric components from field tensors, and finds analytical solutions to the resulting equations.

Contribution

It introduces a self-dual, gauge-invariant formulation of SU(2) gauge theory using a metric tensor derived from field strengths, with analytical solutions.

Findings

Defined a metric tensor from field strength components and duals.

Derived gauge field equations from the metric with constraints.

Obtained two families of analytical solutions.

Abstract

A model of SU(2) gauge theory in the space-time $R\times S^3$ is constructed in terms of local gauge-invariant variables. A metric tensor $g_{\mu \nu}$ is defined starting with the components of the strength tensor $F_{\mu \nu}^k$ and of its dual $\widetilde{F}_{\mu \nu}^k$. It is shown that the components $g_{\mu \nu}$ determine the gauge field equations if some supplementary constraints are imposed. Two families of analitical solutions of the field equations are also obtained.