The Noncommutative Topology of Anti-Self-Dual Gauge Fields

Abstract

Through techniques afforded by $C^{\ast }$-algebras and Hilbert modules, we study the topology of spaces which parametrize families of instanton gauge fields on noncommutative Euclidean four-spheres $S_{\sigma }^4$. By deforming the ADHM construction of instantons on the classical sphere $S^4$, we obtain families of instantons on the quantum sphere which are naturally parametrized by noncommutative topological spaces. Using the internal gauge theory of $S_{\sigma }^4$ determined by the inner automorphisms of its function algebra, we find that one may always recover a classical parameter space by making a suitable choice of internal gauge.

25 pages, no figures; v2 typos corrected, refs updated

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