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Nahm’s transformation for instantons. (English) Zbl 0672.55009
Summary: We describe in mathematical detail the Nahm transformation which maps anti-self dual connections on the four-torus \((S^ 1)^ 4\) onto anti- self-dual connections on the dual torus. This transformation induces a map between the relevant instanton moduli spaces and we show that this map is a (hyper Kähler) isometry.

55R10 Fiber bundles in algebraic topology
81T20 Quantum field theory on curved space or space-time backgrounds
53C05 Connections, general theory
58J99 Partial differential equations on manifolds; differential operators
Full Text: DOI
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