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Segal's contractions, AdS and conformal groups
by Daniel Sternheimer
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Daniel Sternheimer |
| Submission information | |
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| Preprint Link: | scipost_202211_00032v1 (pdf) |
| Date accepted: | 2023-08-28 |
| Date submitted: | 2022-11-17 20:44 |
| Submitted by: | Sternheimer, Daniel |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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Abstract
Symmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the "O'Raifeartaigh theorem", continuing with his incidental introduction in 1951 of the (1953) Inönü—Wigner contractions, of which the passage from AdS (SO(2,3)) to Poincaré is an important example, and with his interest in conformal groups in the latter part of last century. Since the 60s Flato and I had many fruitful interactions with him around these topics. In a last section I succintly relate these interests in symmetries with several of ours, especially elementary particles symmetries and deformation quantization, and with an ongoing program combining both.
Published as SciPost Phys. Proc. 14, 043 (2023)
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Report
This paper is a commemorative reflection on the work and impact of Irving Ezra Segal in group
theoretical methods in physics, and how his ideas have influenced later research lines that nowadays
constitute fundamental tools in mathematical physics. The paper is if historical value, both for the field
and the background of the IGTMP series background, and has been written by a very renowned specialist
which has actually interacted with the late Segal.