无限变形群及其几何和物理应用
Infinite Deformed Groups and Their Geometrical and Physical Applications
摘要：
本文在无限变形群的框架下，给出了任意变曲率几何结构（黎曼空间和具有联络的纤维丛）的Klein程序的实现.这些群利用群变形的思想将规范群推广到了在丛的底空间上的非平凡作用的情形。我们还表明，无限变形群给出了一个群论描述的规范场（引力场与其度量或vierbein部分类似于规范场的内部对称），这是替代他们的几何解释。
英文摘要：
In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of bundles with use of idea of groups deformations. We also show that infinite deformed groups give a group-theoretic description of gauge fields (gravitational field with its metric or vierbein part similarly to gauge fields of internal symmetry) which is alternative for their geometrical interpretation.
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