Hilbert Space Representations of Generalized Canonical Commutation Relations

Asao Arai

Journal of Mathematics, 2013, vol. 2013, 1-7

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:308392

DOI: 10.1155/2013/308392

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