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 \(\widetilde{F}_{\mu \nu}^k\). 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.