Gruppenpest (changes) in nLab
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Context
Physics Quantum systems
physics quantum logic, mathematical physics, philosophy of physics
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theory (physics), model (physics) experiment\linebreak, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories quantum probability theory – observables and states \linebreak \linebreak \linebreak quantum algorithms:
Group Theory
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Classical groups
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Cohomology and Extensions
Related concepts
Contents
Idea
In the late 1920s, Eugene Wigner and Hermann Weyl highlighted the role that group theory and representation theory play in the analysis of quantum mechanics, for instance in the analysis of atomic spectra. While many applications of groups and their representations to quantum physics had more or less explicitly been observed before, Wigner and Weyl stood out as making the mathematical formalism fully explicit. This attitude was not well received by some of their colleagues, who felt that this formal mathematics had no place in physics. In particular Erwin Schrödinger is said (Wigner 1981) to have spoken of the Gruppenpest (German for “plague of group theory”) which ought to be abandoned.
In his autobiography John Slater, an MIT physicist, claimed:
It was at this point that Wigner, Hund, Heitler, and Weyl entered the picture with their “Gruppenpest”: the pest of the group theory… The authors of the “Gruppenpest” wrote papers which were incomprehensible to those like me who had not studied group theory, in which they applied these theoretical results to the study of the many electron problem. The practical consequences appeared to be negligible, but everyone felt that to be in the mainstream one had to learn about it. Yet there were no good texts from which one could learn group theory. It was a frustrating experience, worthy of the name of a pest.
I had what I can only describe as a feeling of outrage at the turn which the subject had taken…
As soon as this [Slaters] paper became known, it was obvious that a great many other physicists were as disgusted as I had been with the group-theoretical approach to the problem. As I heard later, there were remarks made such as “Slater has slain the ‘Gruppenpest’”. I believe that no other piece of work I have done was so universally popular.
Eventually this resistance vanished and turned into its opposite in theoretical fundamental physics: in the classification of fundamental particles by unitary representations of the Poincaré group introduced by Hermann Weyl, in the description of gauge theory in terms of associated bundles given by representations of gauge groups.
Today almost the first thing that one wants to know about any physical theory is its global symmetry-group and gauge group and the their relevant representations.
References
A Historical transcript texts: of an interview with Wigner where he mentions Schrödinger’s remark on theGruppenpest is here:
- Interview with Eugene Wigner by Lillian Hoddeson, Gordon Baym and Frederick Seitz at the New Yorker Hotel January 24, 1981 (Niels Bohr Library and Archives
Hermann Weyl, Quantenmechanik und Gruppentheorie, Zeitschrift für Physik 46 (1927) 1–46 [[doi:10.1007/BF02055756](https://doi.org/10.1007/BF02055756)]
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Hermann Weyl, Gruppentheorie und Quantenmechanik, S. Hirzel, Leipzig, (1931), translated by H. P. Robertson: The Theory of Groups and Quantum Mechanics Dover (1950) [[ISBN:0486602699](https://store.doverpublications.com/0486602699.html), ark:/13960/t1kh1w36w]
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Eugene P. Wigner: Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, Springer (1931) [[doi:10.1007/978-3-663-02555-9](https://doi.org/10.1007/978-3-663-02555-9), pdf]
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Eugene P. Wigner: Group theory: And its application to the quantum mechanics of atomic spectra, 5, Academic Press (1959) [[doi:978-0-12-750550-3](https://www.elsevier.com/books/group-theory/wigner/978-0-12-750550-3)]
A Transcript historical anlysis of Wigner’s an work interview on group theory with a Wigner where he mentions Schrödinger’s remark on theGruppenpest : comment is in
- Arianna Interview Borrelli with and Bretislav Friedrich,Eugene Wigner and the bliss of the “Gruppenpest”Eugene Wigner , ( by Lillian Hoddeson, Gordon Baym and Frederick Seitz at the New Yorker Hotel January 24 (198) [[Niels Bohr Library and Archives](https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4965)]pdf)
For History scholarship on Weyl’s work on group theory and quantum review: mechanics, see
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Erhard Scholz, 2008, Brian G. WybourneWeyl entering the ‘new’ quantum mechanics discourse., In C. Joas, C. Lehner, J. Renn (eds.). HQ-1: Conference on the History of Quantum Physics (Berlin July 2–6, 2007), The “The Gruppen Pest” yesterday, today, and tomorrowPreprint, International Journal of Quantum Chemistry Symp. MPI History of Science Berlin, 350 vol. II, 253–271.7 (1973) 35-43 [[doi:10.1002/qua.560070706](https://doi.org/10.1002/qua.560070706)]
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Erhard Scholz, 2006. Introducting Introducing groups into quantum theory (1926–1930) (1926-1930) , Historia Mathematica 33:440–490,arxiv.org/math.HO/040957133 . 4 (2006) 440-490 [[arXiv:math/0409571](https://arxiv.org/abs/math/0409571),doi:10.1016/j.hm.2005.11.007]
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Christophe Erhard Eckes, Scholz, Weyl and entering the mathematisation ‘new’ of quantum Quantum mechanics Mechanics discourse individual and collective perspectives , ( in: C. Joas, C. Lehner, J. Renn (eds.),slidesHQ-1: Conference on the History of Quantum Physics ). , MPI History of Science Berlin350 II (2008) 253–271. (Berlin July 2–6, 2007) [pdfl]
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John SlaterArianna Borrelli, Bretislav Friedrich, , Eugene Wigner and the bliss of the “Gruppenpest”Solid-State and Molecular Theory: A Scientific Biography (2011) [, Wiley (1975) [[archive](https://archive.org/details/solidstatemolecu00slat/)]pdf]
(in the context of solid state physics and molecular theory)
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Christophe Eckes, Weyl and the mathematisation of Quantum Mechanics individual and collective perspectives (2020) [pdf]
See also:
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John Slater, Solid-State and Molecular Theory: A Scientific Biography, Wiley (1975) [[ark:/13960/t07x0h23t](https://archive.org/details/solidstatemolecu00slat/)]
(in the context of solid state physics and molecular theory)
Last revised on December 2, 2023 at 17:03:53. See the history of this page for a list of all contributions to it.