The Yang–Mills system in compactified Minkowski space; Invariance conditions and SU(2) invariant solutions
1979; American Institute of Physics; Volume: 20; Issue: 5 Linguagem: Inglês
10.1063/1.524141
ISSN1527-2427
AutoresJ. Harnad, Steven Shnider, Luc Vinet,
Tópico(s)Noncommutative and Quantum Gravity Theories
ResumoIn 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:S3→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.
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