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An asymptotic analysis and its application to the nonrelativistic limit of the Pauli–Fierz and a spin-boson model
| Title: | An asymptotic analysis and its application to the nonrelativistic limit of the Pauli–Fierz and a spin-boson model |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | asymptotic solutions | | tensors | | quantum operators | | hilbert space | | quantum electrodynamics | | uses | | fierz--pauli theory | | atoms | | coupling | | radiations | | quantization | | lamb shift |
| Issue Date: | Nov-1990 |
| Publisher: | American Institute of Physics |
| Journal Title: | Journal of Mathematical Physics |
| Volume: | 31 |
| Issue: | 11 |
| Start Page: | 2653 |
| End Page: | 2663 |
| Publisher DOI: | 10.1063/1.528966 |
| Abstract: | An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the Pauli–Fierz model in quantum electrodynamics and of a spin-boson model. It is proven that the resolvent of Hκ converges strongly as κ→∞ and the limit is a pseudoresolvent, which defines an "effective operator" of Hκ at κ≈∞. As corollaries of this result, some limit theorems for Hκ are obtained, including a theorem on spectral concentration. An asymptotic estimate of the infimum of the spectrum (the ground state energy) of Hκ is also given. The application of the abstract theory to the above models yields some new rigorous results for them. |
| Rights: | Copyright © 1990 American Institute of Physics |
| Relation: | http://www.aip.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/13679 |
| 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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