Algebraic structure of quantum fluctuations

On the basis of the existence of second and third moments of fluctuations, we prove a theorem about the Lie-algebraic structure of fluctuation operators. This result gives insight into the quantum character of fluctuations. We illustrate the presence of a Lie algebra of fluctuation operators in a mo...

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Bibliographic Details
Published inJournal of statistical physics Vol. 89; no. 3-4; pp. 633 - 653
Main Authors Momont, B., Verbeure, A., Zagrebnov, V. A.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.11.1997
Subjects
Algebra
Anharmonicity
Existence theorems
Fine structure
Lie groups
Operators (mathematics)
Physics
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Summary:On the basis of the existence of second and third moments of fluctuations, we prove a theorem about the Lie-algebraic structure of fluctuation operators. This result gives insight into the quantum character of fluctuations. We illustrate the presence of a Lie algebra of fluctuation operators in a model of the anharmonic crystal, and show the dependence of the Lie-algebra structure on the fine structure of the fluctuation operator algebra. The result is also applied to construct the normal Goldstone mode in the ideal Bose gas for Bose-Einstein condensation
ISSN:0022-4715
1572-9613
DOI:10.1007/BF02765539