C. N. Yang and contemporary mathematics
type: Item
instance of: scholarly article
title: C. N. Yang and contemporary mathematics
zbMATH Open document ID: 0786.01011
DOI: 10.1007/BF03024319
author: V. Pereyra
published in: The Mathematical Intelligencer
publication date: 1994-05-06T00:00:00Z
review text: 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.
reviewed by: Cristina Irimia
Mathematics Subject Classification ID: 01A65
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 475074
zbMATH Keywords: C. N. Yang
zbMATH Keywords: parity
zbMATH Keywords: nonconservation
zbMATH Keywords: physics
zbMATH Keywords: gauge invariance
zbMATH Keywords: Fermi
zbMATH Keywords: Abelian groups
zbMATH Keywords: Weyl
zbMATH Keywords: gauge fields
zbMATH Keywords: nonintegrable phase factors
zbMATH Keywords: Jim Simons
zbMATH Keywords: fiber bundles
zbMATH Keywords: Yang-Baxter equation
zbMATH Keywords: braid theory
zbMATH Keywords: Hopf algebra
zbMATH Keywords: quantum group
zbMATH Keywords: differential equations
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03024319
OpenAlex ID: W4247714930
description: scientific article; zbMATH DE number 475074