Topological aspects of Yang-Mills theory

  title={Topological aspects of Yang-Mills theory},
  author={M. Atiyah and J. D. Jones},
  journal={Communications in Mathematical Physics},
The space of mapsS3 →G 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). 
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