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The construction of self-dual solutions to SU(2) gauge theory

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Abstract

Ignoring the problem of sources and singularities, explicit expressions are constructed for the ansätze of Atiyah and Ward. These take an especially simple form in theR gauge of Yang. Some non-linear transformation properties of the self-duality equations in this gauge provide an inductive proof of the ansätze. There is a six-parameter family of these Bäcklund transformations. They take real SU(2) gauge fields into real SU(1, 1) gauge fields and vice versa.

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Authors and Affiliations

  1. Laboratorie de Physique Théorique de l'École Normale Supérieure, F-Paris 5, France

    E. F. Corrigan

  2. Department of Mathematics, University of Durham, Durham, U.K.

    D. B. Fairlie & R. G. Yates

  3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW, Cambridge, U.K.

    P. Goddard

Authors
  1. E. F. Corrigan
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  2. D. B. Fairlie
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  3. R. G. Yates
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  4. P. Goddard
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Additional information

Communicated by A. Jaffe

On leave of absence from Department of Mathematics, University of Durham, U.K.

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Corrigan, E.F., Fairlie, D.B., Yates, R.G. et al. The construction of self-dual solutions to SU(2) gauge theory. Commun.Math. Phys. 58, 223–240 (1978). https://doi.org/10.1007/BF01614221

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  • DOI: https://doi.org/10.1007/BF01614221

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