The Yang-mills system in compactified Minkowski space; invariance conditions and SU(2) invariant solutions

J. Harnad; S. Shnider; Luc Vinet

doi:10.1063/1.524141

The Yang-mills system in compactified Minkowski space; invariance conditions and SU(2) invariant solutions

J. Harnad, S. Shnider, Luc Vinet

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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→S³. 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.

Original language	English
Pages (from-to)	931-942
Number of pages	12
Journal	Journal of Mathematical Physics
Volume	20
Issue number	5
DOIs	https://doi.org/10.1063/1.524141
State	Published - 1978
Externally published	Yes

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The Yang-mills system in compactified Minkowski space; invariance conditions and SU(2) invariant solutions

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