Generalized Coherent States Representation

The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-11, Vol.42 (11), p.2608-2614
Main Authors: Kalmetev, R. Sh, Orlov, Yu. N., Sakbaev, V. Zh
Format: Article
Language:English
Subjects:
Algebra
Analysis
Coherence
Commutation
Eigenvalues
Eigenvectors
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators
Probability Theory and Stochastic Processes
Representations
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Summary:The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generalized crowded system. Formulas of covariant symbols of vectors and operators in the representation of generalized coherent states are obtained. It is shown that, similarly to the classical boson case, generalized coherent states are states with minimal uncertainty.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221110123