C. N. Yang and contemporary mathematics
This is an interview taken by D. Z. Zhang to C. N. Yang, Nobel Prize winner in 1957 (together with T. D. Lee), one of the physicists who had greatestly influenced the 20th century progress of mathematics. Pupil of S. S. Chern (former student of his father, K. C. Yang), he studied in USA, and prepared his Ph. D. degree with Fermi (then in Chicago). He realized, by then, that gauge invariance determined all electromagnetic interactions, and tried to generalize the concept to non- Abelian groups (helped by his mate R. L. Mills). Later on, he formulated gauge fields through nonintegrable phase factors, when he first saw the relation between gauge theory and differential geometry (i.e., the similarity between Levi-Civita's parallel displacement and nonintegrable phase factors in gauge fields). The geometer Jim Simons helped him, by saying that gauge theory must be related to connections of fiber bundles. The result was Yang's famous paper Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields''. The other mathematical structure by means of which Yang influenced the development of mathematics was Yang-Baxter equation, discussed in his studies of statistics; it is now applied in knot and braid theory, operator theory, the theory of Hopf algebra, quantum group, monodromy of differential equations.
scientific article; zbMATH DE number 475074
scientific article