平坦空间上Seiberg-Witten和Freund方程的迭代奇异解
Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method
摘要：
虽然众所周知，Seiberg-Witten方程不允许在平坦空间中有非平凡的$L^2$解，但它们的奇异解以前已经在$R^3$中或在降维空间$R^2$和$R^1$中得到了展示，这具有物理意义。在这项工作中，我们采用了一个扩展的霍普夫纤维化，以获得一个迭代过程，以产生特定的奇异解的Seiberg-Witten和Freund方程的平坦空间。通过这种方法获得的解决方案的例子，并简要讨论。
英文摘要：
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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