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Hilbert Space Representations of Generalized Canonical Commutation Relations
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| Title: | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Issue Date: | 2013 |
| Publisher: | Hindawi Publishing Corporation |
| Journal Title: | Journal of Mathematics |
| Volume: | 2013 |
| Start Page: | 1 |
| End Page: | 7 |
| Publisher DOI: | 10.1155/2013/308392 |
| Abstract: | 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. |
| Rights: | Copyright © 2013 Asao Arai. | | http://creativecommons.org/licenses/by-nc-sa/2.1/jp/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/51361 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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