Holonomy和Skyrme模型
Holonomy and Skyrme's model
摘要：
在本文中，我们考虑两个推广的Skyrme模型。一类是从紧三流形到紧李群的映射的变分问题。另一个是平面连接的变分问题。我们描述的路径组件的配置空间的光滑场的每个变分问题。我们证明，分离的路径组件的不变量是定义良好的（不一定顺利）领域有限Skyrme能源。我们证明了，对于这些不变量的每一个可能的值，存在一个极小的Skyrme功能。在整个文件中，我们强调的完整性的Skyrme模型的重要性。一些结果可能在其他情况下是有用的。特别是，我们定义了一个分布平坦的$ L^2_{loc} $连接的holonomy，这种连接的本地开发地图不需要是连续的。
英文摘要：
In this paper we consider two generalizations of the Skyrme model. One is a variational problem for maps from a compact three-manifold to a compact Lie group. The other is a variational problem for flat connections. We describe the path components of the configuration spaces of smooth fields for each of the variational problems. We prove that the invariants separating the path components are well-defined for (not necessarily smooth) fields with finite Skyrme energy. We prove that for every possible value of these invariants there exists a minimizer of the Skyrme functional. Throughout the paper we emphasize the importance of holonomy in the Skyrme model. Some of the results may be useful in other contexts. In particular, we define the holonomy of a distributionally flat $ L^2_{loc} $ connection; the local developing maps for such connections need not be continuous.
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