Hilbert Space Representations of Generalized Canonical Commutation Relations
We consider Hilbert space representations of a generalization of canonical commutation relations , where 's are the elements of an algebra with identity , is the imaginary unit, and is a real number with antisymmetry . Some basic aspects on Hilbert space representations of the generalized CCR...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/308392 |
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| _version_ | 1832553237589262336 |
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| author | Asao Arai |
| author_facet | Asao Arai |
| author_sort | Asao Arai |
| collection | DOAJ |
| description | We consider Hilbert space representations of a generalization of canonical commutation
relations ,
where 's are the elements of an algebra with identity , is the imaginary unit, and is a real number with antisymmetry . Some basic aspects on Hilbert space representations of the generalized CCR (GCCR) are discussed. We
define a Schrödinger-type representation of the GCCR by an analogy with the usual
Schrödinger representation of the CCR with 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. |
| format | Article |
| id | doaj-art-0808b355435145ecbed09233992d3b05 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0808b355435145ecbed09233992d3b052025-02-03T05:54:29ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/308392308392Hilbert Space Representations of Generalized Canonical Commutation RelationsAsao Arai0Department of Mathematics, Hokkaido University, Sapporo 060-0810, JapanWe consider Hilbert space representations of a generalization of canonical commutation relations , where 's are the elements of an algebra with identity , is the imaginary unit, and is a real number with antisymmetry . Some basic aspects on Hilbert space representations of the generalized CCR (GCCR) are discussed. We define a Schrödinger-type representation of the GCCR by an analogy with the usual Schrödinger representation of the CCR with 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.http://dx.doi.org/10.1155/2013/308392 |
| spellingShingle | Asao Arai Hilbert Space Representations of Generalized Canonical Commutation Relations Journal of Mathematics |
| title | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| title_full | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| title_fullStr | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| title_full_unstemmed | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| title_short | Hilbert Space Representations of Generalized Canonical Commutation Relations |
| title_sort | hilbert space representations of generalized canonical commutation relations |
| url | http://dx.doi.org/10.1155/2013/308392 |
| work_keys_str_mv | AT asaoarai hilbertspacerepresentationsofgeneralizedcanonicalcommutationrelations |