有关规范场与纤维丛关系问题的三次阐释

Three Ways to Research on Relationship between Gauge Fields and Fiber Bundles

20世纪末期,先后有四位学者论述了规范场与纤维丛的关系:数学物理学家陆启铿的研究最早发表,它表明抽象数学世界的纤维丛在物理世界获得了规范场这一对应物,纤维丛的客观实在性得到了体现;物理学家吴大峻与杨振宁的研究影响深远,它体现了纤维丛为规范场提供了基础性支持这一思想;数学家陈省身给出了一个本质性的总结:一维纤维的几何表示就是麦克斯韦方程(电磁场),它向二维推广就是杨-米尔斯方程(规范场)。

At the end of the twentieth century, there are four researchers doing the work on the relationship between Gauge fields and fiber bundles. The work of Lu Qikeng is the earliest one. It indicates that fiber bundles have their substance expression in real world. The work of Wu Taitsun and Yang Chengning has the deepest influence in mathematics and physics. It makes clear that fiber bundles give a strong support for gauge fields. The work of Chern Shiingshen has grasped the essence. It finds that fiber bundles on one dimension are electromagnetism fields and fiber bundles on two dimensions are gauge fields.