Abstract
An elementary argument demonstrating the completeness of the Atiyah-Drinfeld-Hitchin-Manin construction of self-dual instanton solutions to Euclidean gauge theories is presented. The adaptation of this discussion to Nahm's construction for SU(2) monopoles is outlined. These constructions are shown to establish a reciprocity or duality between self-dual theories in zero and four dimensions and in one and three dimensions, respectively.
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