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Canonical commutation relations, the Weierstrass Zetafunction, and infinite dimensional Hilbert space representations of the quantum group Uq (sl2)

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83462

Title: Canonical commutation relations, the Weierstrass Zetafunction, and infinite dimensional Hilbert space representations of the quantum group Uq (sl2)
Authors: Arai, A. Browse this author
Issue Date: 1-Nov-1995
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 315
Start Page: 2
End Page: 22
Abstract: A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta-function is considered. The position and the physical momentum operators give a representation of the canonical commutation relations (CCR) with two degrees of freedom. If the charge of the particle is not an integer (the case corresponding to the Aharonov-Bohm effect), then the representation is inequivalent to the Schrodinger representation. It is shown that the inequivalent representation induces infinite dimensional Hilbert space representations of the quantum group Uq(.s[2 ). Some properties of these representations of Uq(s[2 ) are investigated.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69066
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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