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

Arai, Asao

Journal of Mathematical Physics, 1996, 37(9), 4203-4218

Permalink : https://hdl.handle.net/2115/13672

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アクセス権	open access
URI	https://hdl.handle.net/2115/13672
タイトル	Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group Uq(sl2)
著者	e-Rad_Researcher 80134807 著者名 Arai, Asao
言語	英語
キーワード	lie groups
	commutation relations
	hilbert space
	charged particles
	schroedinger picture
	aharonov-bohm effect
	unitarity
	algebras
発行日	1996-09
出版者	American Institute of Physics
収録物名	Journal of Mathematical Physics
巻(号)	37(9)
ページ	4203-4218
抄録	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 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 Schrödinger representation. It is shown that the inequivalent representation induces infinite-dimensional Hilbert space representations of the quantum group Uq(sl2). Some properties of these representations of Uq(sl2) are investigated.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	Copyright © 1996 American Institute of Physics
PISSN	0022-2488
EISSN	1089-7658
関連情報	URI http://www.aip.org/
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1063/1.531797