Conclusions
Representations of an associative countably generated*-algebra by unbounded operators must be analyzed not only in connection with representations of canonical variables in quantum theory but also in different questions of the theory of representations of finite-dimensional and some infinite-dimensional Lie groups (in a consideration of the corresponding Lie algebras). In all such cases our theorem on the decomposition of unbounded representations into irreducible (factor) representations can be used.
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Additional information
A. A. Zhdanov Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 19, No. 1, pp. 27–36, April, 1974.
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Borisov, N.V. Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom. Theor Math Phys 19, 325–331 (1974). https://doi.org/10.1007/BF01037188
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DOI: https://doi.org/10.1007/BF01037188