Communications in Mathematical Physics

, Volume 55, Issue 2, pp 117–124 | Cite as

Instantons and algebraic geometry

  • M. F. Atiyah
  • R. S. Ward
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Algebraic Geometry 
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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • M. F. Atiyah
    • 1
  • R. S. Ward
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordEngland

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