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A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum Fields
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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