Communications in Mathematical Physics

, Volume 61, Issue 2, pp 97–118 | Cite as

Topological aspects of Yang-Mills theory

  • M. F. Atiyah
  • J. D. S. Jones


The space of mapsS3G has components which give the topological quantum number of Yang-Mills theory for the groupG. Each component of the space has further topological invariants. WhenG=SU(2) we show that these invariants (the homology groups) are “captured” by the space of instantons. Using these invariants we show that potentials must exist for which the massless Dirac equation (in Euclidean 4-space) has arbitrarily many independent solutions (for fixed instanton number).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Number 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • M. F. Atiyah
    • 1
  • J. D. S. Jones
    • 2
  1. 1.Mathematical InstituteUniversity of OxfordOxfordEngland
  2. 2.Magdalen CollegeOxfordEngland

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