Summary
We describe the contractions of the rotation algebra. A special singular one is analyzed; it yields the Heisenberg algebra. The unitary representation of the latter is obtained by contracting representations of the rotation algebra using Inönü and Wigner's trick.
Riassunto
Si descrivono le contrazioni dell'algebra delle rotazioni. Se ne studia una singolare speciale; essa dà l'algebra di Heisenberg. Si ottiene la rappresentazione unitaria di quest'ultima contraendo le rappresentazioni dell'algebra delle rotazioni coll'artificio di Wigner e Inönü.
Резюме
Мы описываем сокращения алгебры вращения. Анализируется специальная сингулярная алгебра, что даёт алгебру Гайзенберга. Выводится унитарное представление для алгебры Гайзенберга, посредством сокращения представлений алгебры вращения, используя приёню и Вигнера.
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References
I. E. Segal:Duke Math. Journ.,48, 221 (1951); inLes problèmes mathématiques dans la théorie quantique des champs (Paris, 1958).
E. Inönü andE. P. Wigner:Proc. Nat. Acad. Sci.,39, 510 (1953).
G. Berendt:Lectures on Contractions of Algebras. Istanbul Summer Institute, 1966.
N. Jacobson:Lie Algebras (New York, 1962).
J. von Neumann:Matematische Grundlagen der Quatenmechanik (Berlin, 1932).
G. Mackey:Bull. Am. Math. Soc.,56, 385 (1950).
A. Messiah:Mécanique quantique, vol.1 (Paris, 1961).
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On leave of absence from the University of Zaragoza, Spain.
The research reported in this paper was supported in part by the National Science Foundation.
Traduzione a cura della Redazione.
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Ynduráin, F.J. The Heisenberg algebra and contractions of the rotation algebra. Il Nuovo Cimento A (1965-1970) 50, 308–312 (1967). https://doi.org/10.1007/BF02827738
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DOI: https://doi.org/10.1007/BF02827738