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This article is cited in 3 scientific papers (total in 3 papers)
Representations of general commutation relations
V. V. Vedenyapina, O. V. Mingalevb, I. V. Mingalevb a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
b Polar Geophysical Institute
Abstract:
General commutation relations involving creation, annihilation, and particle number operators are considered. Such commutation relations arise in the context of nonstandard Poisson brackets. All possible types of irreducible representations in which the particle number operator or the product of the creation and annihilation operators has a basis of orthonormal eigenvectors are constructed. The irreducible representations that involve the particle number operator reduce to one of four types and those that do not involve the particle number operator reduce to one of five types.
Received: 14.12.1995 Revised: 16.04.1997
Citation:
V. V. Vedenyapin, O. V. Mingalev, I. V. Mingalev, “Representations of general commutation relations”, TMF, 113:3 (1997), 369–383; Theoret. and Math. Phys., 113:3 (1997), 1508–1519
Linking options:
https://www.mathnet.ru/eng/tmf1086https://doi.org/10.4213/tmf1086 https://www.mathnet.ru/eng/tmf/v113/i3/p369
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