nLab Chen Ning Yang

• Wikipedia entry

Selected writings

Introducing Yang-Mills theory (eventually: quantum chromodynamics):

• Chen Ning Yang, Robert Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance. Physical Review 96 (1): 191– 195. (1954) (web)

On the braid group, knot theory and braid representations via the quantum Yang-Baxter equation:

• Chen Ning Yang, M. L. Ge (eds.), Braid Group, Knot Theory and Statistical Mechanics, Advanced Series in Mathematical Physics 9, World Scientific (1991) [doi:10.1142/0796]

On the Aharonov-Bohm effect, generalized to non-abelian Yang-Mills theory and its description by connections on fiber bundles in physics:

• Tai Tsun Wu, Chen Ning Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D 12 (1975) 3845 [doi:10.1103/PhysRevD.12.3845]

On Dirac monopoles:

• Tai Tsun Wu, Chen Ning Yang, Dirac monopole without strings: monopole harmonics, Nuclear Physics B107:3 (1976) 365–380

• Tai Tsun Wu, Chen Ning Yang, Dirac’s monopole without strings: Classical Lagrangian theory, Phys. Rev. D 14, 437 (1976)

On the historical origin of Maxwell's equations, the “vector potential” and (Yang-Mills) gauge theory:

• A. C. T. Wu, Chen Ning Yang, Evolution of the concept of vector potential in the description of the fundamental interactions, International Journal of Modern Physics A 21 16 (2006) 3235-3277 [doi:10.1142/S0217751X06033143]

• Chen Ning Yang, The conceptual origins of Maxwell’s equations and gauge theory, Phyics Today 67 11 (2014) [doi:10.1063/PT.3.2585, pdf]

Quotes

On Yang-Mills theory (gauge theory) being about connections on principal bundles/fiber bundles:

Yang wrote in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567:

In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

Yang expanded on this passage in an interview recorded as

• D. Z. Zhang, C. N. Yang and contemporary mathematics, The Mathematical Intelligencer 15, 13–21 (1993) (doi:10.1007/BF03024319):

$[$This$]$ was not just joy. There was something more, something deeper: After all, what could be more mysterious, what could be more awe-inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?

Related entries

• Yang-Mills theory

• Yang monopole

category: people