Geodesic
Representations of general commutation relations
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 369-383

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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. 
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     author = {V. V. Vedenyapin and O. V. Mingalev and I. V. Mingalev},
     title = {Representations of general commutation relations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {113},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a1/}
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V. V. Vedenyapin; O. V. Mingalev; I. V. Mingalev. Representations of general commutation relations. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 369-383. http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a1/