Joint extension of states of subsystems for a CAR system

Huzihiro Araki, Hajime Moriya

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a Fermion system, where a novel feature is non-commutativity between algebras of subsystems. For an arbitrary (finite or infinite) number of given subsystems, a product state extension is shown to exist if and only if all states of subsystems except at most one are even (with respect to the Fermion number). If the states of all subsystems are pure, then the same condition is shown to be necessary and sufficient for the existence of any joint extension. If the condition holds, the unique product state extension is the only joint extension. For a pair of subsystems, with one of the given subsystem states pure, a necessary and sufficient condition for the existence of a joint extension and the form of all joint extensions (unique for almost all cases) are given. For a pair of subsystems with non-pure subsystem states, some classes of examples of joint extensions are given where non-uniqueness of joint extensions prevails.

Original languageEnglish
Pages (from-to)105-122
Number of pages18
JournalCommunications in Mathematical Physics
Volume237
Issue number1-2
Publication statusPublished - 2003 Jun
Externally publishedYes

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fermions
uniqueness
products
constrictions
algebra

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Joint extension of states of subsystems for a CAR system. / Araki, Huzihiro; Moriya, Hajime.

In: Communications in Mathematical Physics, Vol. 237, No. 1-2, 06.2003, p. 105-122.

Research output: Contribution to journalArticle

Araki, H & Moriya, H 2003, 'Joint extension of states of subsystems for a CAR system', Communications in Mathematical Physics, vol. 237, no. 1-2, pp. 105-122.
Araki, Huzihiro ; Moriya, Hajime. / Joint extension of states of subsystems for a CAR system. In: Communications in Mathematical Physics. 2003 ; Vol. 237, No. 1-2. pp. 105-122.
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