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 
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/
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     title = {Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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