### Abstract

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.

Original language | English |
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Pages (from-to) | 325-331 |

Number of pages | 7 |

Journal | Theoretical and Mathematical Physics |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Apr 1974 |

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### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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**Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom.** / Borisov, N. V.

Research output

TY - JOUR

T1 - Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom

AU - Borisov, N. V.

PY - 1974/4/1

Y1 - 1974/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34250396062&partnerID=8YFLogxK

U2 - 10.1007/BF01037188

DO - 10.1007/BF01037188

M3 - Article

AN - SCOPUS:34250396062

VL - 19

SP - 325

EP - 331

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 1

ER -