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

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 $g_{μν}$ is defined starting with the components of the strength tensor $F_{μν}^k$ and of its dual $\widetilde{F}_{μν}^k$. It is shown that the components $g_{μν}$ determine the gauge field equations if some supplementary constraints are imposed. Two families of analitical solutions of the field equations are also obtained.