Hilbert Space Representations of Generalized Canonical Commutation Relations
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-01-17
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We consider Hilbert space representations of a generalization of canonical commutation relations (CCRs):[Xj,Xk]:=XjXk−XkXj=iΘjkI (j,k=1,2,…,2n), where Xj's are the elements of an algebra with identity I, i is the imaginary unit, and Θjk is a real number with antisymmetry Θjk=−Θkj (k,j=1,2,…,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 an 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.
American Psychological Association (APA)
Arai, Asao. 2013. Hilbert Space Representations of Generalized Canonical Commutation Relations. Journal of Mathematics،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-462259
Modern Language Association (MLA)
Arai, Asao. Hilbert Space Representations of Generalized Canonical Commutation Relations. Journal of Mathematics No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-462259
American Medical Association (AMA)
Arai, Asao. Hilbert Space Representations of Generalized Canonical Commutation Relations. Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-462259
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-462259