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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 →KAKEN DB |
| Issue Date: | 1-Jun-2014 |
| Publisher: | Springer |
| Journal Title: | Annales Henri Poincare |
| Volume: | 15 |
| Issue: | 6 |
| Start Page: | 1145 |
| End Page: | 1170 |
| Publisher DOI: | 10.1007/s00023-013-0271-7 |
| Abstract: | Let H (0) and H (I) be a self-adjoint and a symmetric operator on a complex Hilbert space, respectively, and suppose that H (0) is bounded below and the infimum E (0) of the spectrum of H (0) is a simple eigenvalue of H (0) which is not necessarily isolated. In this paper, we present a new asymptotic perturbation theory for an eigenvalue E(lambda) of the operator satisfying lim (lambda -> 0) E(lambda) = E (0). The point of the theory is in that it covers also the case where E (0) is a non-isolated eigenvalue of H (0). Under a suitable set of assumptions, we derive an asymptotic expansion of E(lambda) up to an arbitrary finite order of lambda as lambda -> 0. We apply the abstract results to a model of massless quantum fields, called the generalized spin-boson model (Arai and Hirokawa in J Funct Anal 151:455-503, 1997) and show that the ground-state energy of the model has asymptotic expansions in the coupling constant lambda as lambda -> 0. |
| Rights: | The final publication is available at link.springer.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/59115 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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