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

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 ${\tilde{F}}_{\mu \nu }^k$. 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.