Geodesic
Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom
Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 1, pp. 27-36

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It is shown that any representation Of canonical variables, (i.e., a representation of the canonical commutation relations in the Heisenberg form) is a direct integral of irreducible (factor) representations; no assumptions are made concerning the possibility of a transition to the Weyl form of the commutation relations. This theorem is applied to the construction of decompositions into irreducible (factor) representations of any finite-dimensional and some inifinitedimensional Lie algebras by unbounded operators in Hilbert space. The need for such decompositions arises in the harmonic analysis of unitary representations of the corresponding Lie groups. 
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     author = {N. V. Borisov},
     title = {Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {27--36},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_19_1_a2/}
}
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N. V. Borisov. Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom. Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 1, pp. 27-36. http://geodesic.mathdoc.fr/item/TMF_1974_19_1_a2/