Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that
Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that
复制标题
黎曼几何、纤维束、卡鲁扎-克莱因理论等等
DOI：
10.1142/0488
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发表时间：
1988
影响因子：
5
通讯作者：
A. Jadczyk
中科院分区：
文献类型：
--
作者：
R. Coquereaux;A. Jadczyk
本书讨论了卡鲁扎-克莱因理论的几何方面。这十章涵盖了从微分和黎曼流形到爱因斯坦-杨-米尔斯作用约化的主题。对于理论和实验物理学家和数学家来说，这绝对是一本有趣的读物。内容：一般性；李群的黎曼几何；齐次空间黎曼几何； （右）主丛的黎曼几何；纤维丛的黎曼几何和李群 G 的给定作用；物质场的几何；谐波分析和降维；正交丛和自旋丛的降维； Einstein-Yang-Mills 系统的 G 不变性；一群团体的行动。
This book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental. Contents: Generalities; Riemannian Geometry of Lie Groups; Riemannian Geometry of Homogeneous Spaces; Riemannian Geometry of a (Right) Principal Bundle; Riemannian Geometry of a Bundle with Fibers and a Given Action of a Lie Group G; Geometry of Matter Fields; Harmonic Analysis and Dimensional Reduction; Dimensional Reduction of the Orthogonal Bundle and of the Spin Bundles; G-Invariance of Einstein-Yang-Mills Systems; Action of a Bundle of Groups.