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Weyl algebra and a realization of the unitary symmetry

Strasburger, Aleksander — 1998

Proceedings of the 17th Winter School "Geometry and Physics"

In the paper the origins of the intrinsic unitary symmetry encountered in the study of bosonic systems with finite degrees of freedom and its relations with the Weyl algebra (1979, Jacobson) generated by the quantum canonical commutation relations are presented. An analytical representation of the Weyl algebra formulated in terms of partial differential operators with polynomial coefficients is studied in detail. As a basic example, the symmetry properties of the d -dimensional quantum harmonic oscillator...

Inducing spherical representations of semi-simple Lie groups

Aleksander Strasburger — 1975

ContentsIntroduction............................................................................................................................................................................... 5Chapter I. Preliminaries and notations....................................................................................................................... 8    1. Manifolds—generalities................................................................................................. 8    2. Representations................................................................................................................

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