2023-03-26T22:44:13Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698282022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum FieldsArai, Asaoopen accessasymptotic perturbation theoryembedded eigenvaluegeneralized spin-boson modelground state energynon-isolated eigenvaluemassless quantum field410Let 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.Department of Mathematics, Hokkaido University2012-12-07engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84169http://hdl.handle.net/2115/6982810.14943/84169Hokkaido University Preprint Series in Mathematics1023129https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69828/1/pre1023.pdfapplication/pdf167.83 KB2012-12-07