Topological aspects of Yang-Mills theory |
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Authors: | M. F. Atiyah J. D. S. Jones |
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Affiliation: | (1) Mathematical Institute, University of Oxford, OX1 3LB Oxford, England;(2) Magdalen College, OX1 3LB Oxford, England |
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Abstract: | 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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