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arXiv · hep-th/0306263

Noncommutative Monopoles and Riemann-Hilbert Problems

Olaf Lechtenfeld·Alexander D. Popov
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Abstract

The Bogomolny equations for Yang-Mills-Higgs monopoles follow from a system of linear equations which may be solved through a parametric Riemann-Hilbert problem. We extend this approach to noncommutative R^3 and use it to (re)construct noncommutative Dirac, Wu-Yang, and BPS monopole configurations in a unified manner. In all cases we write down the underlying matrix-valued functions for multi-monopoles and solve the corresponding Riemann-Hilbert problems for charge one.

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Olaf Lechtenfeld, Alexander D. Popov. 2004-02-12. Noncommutative Monopoles and Riemann-Hilbert Problems. https://doi.org/10.1088/1126-6708%2F2004%2F01%2F069

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