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Instantons and algebraic geometry

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Abstract

Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsätzeA l forl≧1.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, OX1 3LB, Oxford, England

    M. F. Atiyah & R. S. Ward

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  1. M. F. Atiyah
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  2. R. S. Ward
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Communicated by R. Stora

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Atiyah, M.F., Ward, R.S. Instantons and algebraic geometry. Commun.Math. Phys. 55, 117–124 (1977). https://doi.org/10.1007/BF01626514

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  • DOI: https://doi.org/10.1007/BF01626514

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