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A model of gauge theory with invariant variables. (English) Zbl 1105.83302
Summary: A model for \(SU\)(2) gauge theory with invariant variables is presented. The strength tensor of the \(SU\)(2) gauge potentials and its Hodge dual are obtained for a spherical symmetric model. Then, a metric tensor associated to these tensors is constructed. The components of this metric tensor are interpreted as gauge invariant variables for \(SU\)(2) theory. The property of self -duality of the gauge model with respect to the metric tensor is studied. The self-duality equations are written and their solution is obtained. A comparison with the Yang-Mills field equations is also given.
MSC:
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81T13 Yang-Mills and other gauge theories in quantum field theory
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
83C22 Einstein-Maxwell equations
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