Entropy, the central limit theorem and the algebra of the canonical commutation relation

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3 Citations (Scopus)

Abstract

The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state ψ, the weighted convolutions ψn of the central limit tend to the quasi-free reduction ψQ of ψ pointwise. It is proved that if the initial relative entropy S(ψ,ψQ) is finite, then S(ψnQ) goes to 0 and so {norm of matrix}ψnQ{norm of matrix}→0. No restriction on the dimension of the test function space is made.

Original languageEnglish
Pages (from-to)211-220
Number of pages10
JournalLetters in Mathematical Physics
Volume24
Issue number3
DOIs
Publication statusPublished - Mar 1 1992

Keywords

  • Mathematics Subject Classification (1991): 82B10

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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