Abstract
We review the definition of instanton (= pseudoparticle) solutions and their importance in the context of nonabelian gauge (= Yang-Mills) theories, as well as the recent progress, due to Atiyah and Ward, in their construction, using the Penrose twistor transform and methods of algebraic geometry. In particular, we present a proof of the theorem of Atiyah and Ward on the correspondence between SU(2) instanton solutions over the 4-sphere and certain algebraic 2-dimensional complex vector bundles over complex projective 3-space.
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