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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |