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Self-dual Yang-Mills fields ind=4 and integrable systems in 1≤d≤3

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Abstract

The Ward correspondence between self-dual Yang-Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang-Mills model ind=4 with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension 1≤d≤3. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.

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Authors
  1. T. A. Ivanova
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  2. A. D. Popov
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Additional information

N. N. Bogolyubov Theoretical Physics Laboratory, JINR, 141980 Dubna, Russia. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 384–419, March, 1995.

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Ivanova, T.A., Popov, A.D. Self-dual Yang-Mills fields ind=4 and integrable systems in 1≤d≤3. Theor Math Phys 102, 280–304 (1995). https://doi.org/10.1007/BF01017880

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