Joint extension of states of subsystems for a CAR system

Huzihiro Araki, Hajime Moriya

研究成果: Article査読

20 被引用数 (Scopus)


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.

ジャーナルCommunications in Mathematical Physics
出版ステータスPublished - 2003 6

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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