纤维丛是一门研究复杂系统的数学理论，用于描述许多深刻的数学和物理现象，已广泛应用在微分几何、拓扑学、物理学和信息学等领域。文章简述了纤维丛的起源、基本概念和理论基础，结合实例介绍了其在多个领域的应用。
Fiber bundles theory is a mathematical tool to study complex systems and describes profound mathematical and physical phenomena. It has been widely applied in various fields such as differential geometry, topology, physics, and informatics. This article provides a brief overview of the origin, fundamental concepts, and theoretical foundations of fiber bundles theory, and showcases its applications in multiple domains through examples.
[1] BERNSTEIN H J, PHILLIPS A V. Fiber bundles and quantum theory [J]. Scientific American, 1981, 245(1): 122-137.
[2] SCHWICHTENBERG J. Physics from finance: A gentle introduction to gauge theories, fundamental interactions and fiber bundles [M]. Independently Published, 2019.
[3] 桂起权, 高策, 李继堂, 等. 规范场论的哲学探究: 它的概念基础、历史发展与哲学意蕴[M]. 北京: 科学出版社, 2008.
[4] AUYANG S Y. How is quantum field theory possible? [M]. New York: Oxford University Press, 1995.
