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On a generalised Fourier transform of instantons over flat tori. (English) Zbl 0651.58042

Summary: Recently P. Braam pointed out that Nahm’s adaption of the ADHM procedure to the case of monopoles equally well applies to instantons over flat tori, relating them to instantons over the first Brillouin zone. We show that this construction has an inverse. Hence the Nahm transform actually is a duality transform.

MSC:

58Z05 Applications of global analysis to the sciences
58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
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