Hilbert Space Representations of Generalized Canonical Commutation Relations

Arai, Asao

Journal of Mathematics, 2013, 2013, 1-7

Permalink : https://hdl.handle.net/2115/51361

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アクセス権	open access
URI	https://hdl.handle.net/2115/51361
タイトル	Hilbert Space Representations of Generalized Canonical Commutation Relations
著者	e-Rad_Researcher 80134807 著者名 Arai, Asao
言語	英語
発行日	2013
出版者	Hindawi Publishing Corporation
収録物名	Journal of Mathematics
巻(号)	2013
ページ	1-7
抄録	We consider Hilbert space representations of a generalization of canonical commutation relations (CCR): [Xj ,Xk] := XjXk ¡ XkXj = iΘjkI (j, k = 1, 2, . . . , 2n), where Xj ’s are elements of an algebra with identity I, i is the imaginary unit, and Θjk is a real number with Θjk = ¡Θkj (j, k = 1, . . . , 2n). Some basic aspects on Hilbert space representations of the generalized CCR (GCCR) are discussed. We define a Schr¨odinger type representation of the GCCR by analogy with the usual Schr¨odinger representation of the CCR with n degrees of freedom. Also we introduce a Weyl type representation of the GCCR. The main result of the present paper is a uniqueness theorem on Weyl representations of the GCCR.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	Creative Commons Attribution-NonCommercial-ShareAlike 2.1 Japan
権利情報	Copyright © 2013 Asao Arai.
PISSN	2314-4629
EISSN	2314-4785
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1155/2013/308392