Monopoles and Projective Representations: Two Areas of Influence of Yang-Mills Theory on Mathematics

2004/05/18 by Stephen L. Adler, Adler, Stephen L.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP #physics.hist-ph

paper · pdf · doi:10.48550/arxiv.math-ph/0405049

8 pages; for a volume on the influence of Yang-Mills theory on mathematics, G. 't Hooft and W. Nahm, eds., to be published by World Scientific. Final version; references added

openalex publication_date 2004/05/18 · arxiv created 2004/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I describe how my involvement with monopoles related to the multimonopole existence proof of Taubes, and how my later work on quaternionic quantum mechanics led to the classification theorem for generalized projective group representations of Tao and Millard.

Citations

• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

Related

• Monopoles in arbitrary dimension
• Monopole condensates in SU(N) Yang-Mills Theory
• An overview of the history of projective representations (spin representations) of groups
• Dirac-Yang monopoles and their regular counterparts
• SU(N) monopoles with and without SUSY