Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Hilbert Space Representations of Generalized Canonical Commutation Relations
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
|
Submitter: 数学紀要登録作業用
|