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Topological aspects of Yang-Mills theory

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Abstract

The space of mapsS 3 →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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Authors and Affiliations

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

    M. F. Atiyah

  2. Magdalen College, OX1 3LB, Oxford, England

    J. D. S. Jones

Authors
  1. M. F. Atiyah
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  2. J. D. S. Jones
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Communicated by A. Jaffe

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Atiyah, M.F., Jones, J.D.S. Topological aspects of Yang-Mills theory. Commun.Math. Phys. 61, 97–118 (1978). https://doi.org/10.1007/BF01609489

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