Monopoles and Projective Representations: Two Areas of Influence of Yang–mills Theory on Mathematics
نویسندگان
چکیده
In this essay I discuss two unrelated subjects with a common theme: the influence of Yang–Mills theory on mathematics. In the first part I describe how my interest in monopole solutions in the period 1978–1980 led indirectly to the completion by Clifford Taubes of his multimonopole existence theorem during a visit to the Institute for Advanced Study in the spring of 1980. In the second part I shift my focus to a generalized definition of projective group representations that I proposed in the context of quaternionic quantum mechanics. This inspired a classification theorem proved by Terry Tao and Andrew Millard in 1996, which has useful implications for projective representations in standard, complex quantum mechanics.
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