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Annals of Physics

Generalized Schrödinger representations

Published Jan 1, 1969• 0 citations
Publisher
DOI
10.1016/0003-4916(69)90354-6

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Journal of Mathematics•Jan 1, 2013•5 citations
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.