Ground states of a general class of quantum field Hamiltonians

Asao Arai, Masao Hirokawa

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30 Citations (Scopus)

Abstract

We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(ν) with a parameter ν ≥ 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(ν) and those of H by formulating sufficient conditions under which weak limits, as ν → 0, of the ground states of H(ν)'s are those of H. We also establish existence theorems on ground states of H(ν) and H under weaker conditions than in the previous paper mentioned above.

Original languageEnglish
Pages (from-to)1085-1135
Number of pages51
JournalReviews in Mathematical Physics
Volume12
Issue number8
DOIs
Publication statusPublished - Aug 2000
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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