The Yang–Mills system in compactified Minkowski space; Invariance conditions and SU(2) invariant solutions

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Abstract
In this work the SU(2) Yang–Mills equations are studied in compactified Minkowski space. The manifold is identified with that of the Lie group U(1) ×SU(2) and a classification is made of all SU(2) principal bundles over this base space in terms of homotopy classes of mappings f:S 3→S 3. Invariance of gauge fields under transformation groups is defined in terms of bundle mappings and the case of invariance under SU(2) translations is shown to imply a trivial bundle structure. All solutions to the field equations invariant under U(1) ×SU(2) translations are obtained as well as all (anti‐) self‐dual solutions invariant under SU(2) translations.