On Quasifree States of the Canonical Commutation Relations (I) | Zendy

Huzihiro Araki | Zendy; Masafumi Shiraishi | Zendy

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On Quasifree States of the Canonical Commutation Relations (I)

Author(s) -

Huzihiro Araki,

Masafumi Shiraishi

Publication year - 1971

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195193785

Subject(s) - equivalence (formal languages) , mathematics , commutation , generalization , algebra over a field , equivalence relation , dual (grammatical number) , canonical form , pure mathematics , representation (politics) , physics , mathematical analysis , quantum mechanics , linguistics , voltage , philosophy , politics , political science , law

A nece?sar> and sufficient condition for the qu?H-equivalence of two quasifree primary representations of the canonical commutation relations is derived. A quasifree state of the self-dual CCR algebra 2f.(^3 Y, F\ which is a slight generalization of conventional canonical commutation relations, has been discussed in the preceding work Ql], In the present paper, we derive a necessary and sufficient condition for the quasi-equivalence of representations associated with quasifree states, when the representation is primary (i.e. the associated von Neumann algebra is a factor). We believe that the following features of the present analysis is worth mentioning.

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