Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method

Details Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method

2005-11-10

arxiv.org/abs/math-ph/0511038v2

J.Math.Phys. 47 (2006) 013514

Physics

Mathematical Physics

7 pages, minor changes. To appear in J. Math. Phys

Scientific paper

10.1063/1.2162823

Although it is well known that the Seiberg-Witten equations do not admit nontrivial $L^2$ solutions in flat space, singular solutions to them have been previously exhibited -- either in $R^3$ or in the dimensionally reduced spaces $R^2$ and $R^1$ -- which have physical interest. In this work, we employ an extension of the Hopf fibration to obtain an iterative procedure to generate particular singular solutions to the Seiberg-Witten and Freund equations on flat space. Examples of solutions obtained by such method are presented and briefly discussed.

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