论文标题
HOPF振动的基本介绍
An Elementary Introduction to the Hopf Fibration
论文作者
论文摘要
HOPF振动是数学和物理学中的重要对象。 HOPF纤维纤维中的拓扑结构和谎言理论理论的基本对象具有里程碑意义的发现，具有多种物理应用，包括磁性单极，刚体机械和量子信息理论。这篇说明性文章介绍了本科生可以使用的HOPF纤维化介绍。我们使用四元素代数来说明HOPF纤维的代数和几何特性以及与3空间旋转的连接，这是物理和工程自然应用的基础。
The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic monopoles, rigid body mechanics, and quantum information theory. This expository article presents an introduction to the Hopf fibration that is accessible to undergraduate students. We use the algebra of quaternions to illustrate algebraic and geometric properties of the Hopf fibration and the connection with rotations of 3-space that is the basis for natural applications to physics and engineering.
