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A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum Fields

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84169

Title: A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum Fields
Authors: Arai, Asao Browse this author
Keywords: asymptotic perturbation theory
embedded eigenvalue
generalized spin-boson model
ground state energy
non-isolated eigenvalue
massless quantum field
Issue Date: 7-Dec-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1023
Start Page: 1
End Page: 29
Abstract: Let H0 and HI be a self-adjoint and a symmetric operator on a complex Hilbert space, respectively, and suppose that H0 is bounded below and the infimum E0 of the spectrum of H0 is a simple eigenvalue of H0 which is not necessarily isolated. In this paper, we present a new asymptotic perturbation theory for an eigenvalue E(λ) of the operator H(λ) := H0 +λHI (λ 2 Rn f0g) satisfying limλ!0 E(λ) = E0. The point of the theory is in that it covers also the case where E0 is a non-isolated eigenvalue of H0. Under a suitable set of assumptions, we derive an asymptotic expansion of E(λ) up to an arbitrary finite order of λ as λ ! 0. We apply the abstract results to a model of massless quantum fields, called the generalized spinboson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455–503) and show that the ground state energy of the model has asymptotic expansions in the coupling constant λ as λ ! 0.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69828
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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