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Hilbert Space Representations of Generalized Canonical Commutation Relations

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84164

Title: Hilbert Space Representations of Generalized Canonical Commutation Relations
Authors: Arai, Asao Browse this author
Keywords: canonical commutation relations
generalized canonical commutation relations
quantum space
quantum phase space
non-commutative space-time
Issue Date: 26-Sep-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1018
Start Page: 1
End Page: 15
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 Schrödinger type representation of the GCCR by analogy with the usual Schrödinger 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69823
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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