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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of the canonical commutation and anticommutation relations


Author: Steven Robbins
Journal: Proc. Amer. Math. Soc. 71 (1978), 85-88
MSC: Primary 47B47
DOI: https://doi.org/10.1090/S0002-9939-1978-0482363-2
MathSciNet review: 0482363
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Abstract: The relation $ {C^ \ast }C{C^ \ast } - {C^ \ast } = C{C^{ \ast 2}}$ involving a closed densely defined operator C generalizes both the canonical commutation relation of bosons and the canonical anticommutation relation of fermions. It is shown that the operators satisfying this relation can be classified by an index $ p,p = 0,1,2, \ldots ,\infty $.


References [Enhancements On Off] (What's this?)

  • [1] C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag New York, Inc., New York, 1967. MR 0217618

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0482363-2
Keywords: Canonical commutation relations, canonical anticommutation relation
Article copyright: © Copyright 1978 American Mathematical Society