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Comments on the \(U(2)\) noncommutative instanton. (English) Zbl 0971.81079

Summary: We discuss the ’t Hoft ansatz for instanton solutions in noncommutative \(U(2)\) Yang-Mills theory. We show that the extension of the ansatz leading to singular solutions in the commutative case, yields to non self-dual (or self-antidual) configurations in noncommutative space-time. A proposal leading to self-dual solutions with \(Q=1\) topological charge (the equivalent of the regular BPST ansatz) can be engineered, but in that case the gauge field and the curvature are not Hermitian (although the resulting Lagrangian is real).

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T75 Noncommutative geometry methods in quantum field theory
58D29 Moduli problems for topological structures
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