| Project/Area Number |
15540191
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Setsunan University |
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Principal Investigator |
HIROSHIMA Fumio Setsunan University, Fuculty of Engeneering, Advanced Proffesor, 工学部, 助教授 (00330358)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Keichi Setsunan University, Fuculty of Engeneering, Proffesor, 工学部, 教授 (50268489)
TERAMOTO Yoshiaki Setsunan University, Fuculty of Engeneering, Advanced Proffesor, 工学部, 助教授 (40237011)
SHIMADA Shin-ichi Setsunan University, Fuculty of Engeneering, Advanced Proffesor, 工学部, 助教授 (40196481)
HIROKAWA Masao Okayama University, Fuculty of Science, Professor, 理学部, 教授 (70282788)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Ground states / Asymptotic fields / Spectral scattring theory / Mass renormalization / QED / Number operators / Carleman operators / Multiplicity / ハシルトニアン / スペクトル解析 / 赤外・紫外発散 / ギブス測度 / くりこみ |
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| Research Abstract |
The spectrum of Hamiltonians describing a system of charged particles interacting with a quantum field is nonpertubatively studied. It can be regarded as the spectral analysis of a self-adjoint operator on a tensor product of infinite dimensional Hilbert spaces. Mainly an electron minimally coupled with photons, and the so-called Nelson model are investigated by means of functional analysis and functional integrals. The purpos of the present project is as follows : (1)estimates of the number of bosons in ground states, (2)to prove the tightness of Gibbs measures, (3)estimates of the multiplicity of ground states of a Hamiltonian without cutoffs, (4)the decay of the Green functions of a certain spin model. Our achievements are as follows.
For (1)by virtute of an application of asymptotic fields of spectral scattering theory in the quantum field theory we got some results which are submitted as the paper entitled
Regularities of ground states in quantum field models (with Arai and Hirokawa)
For (2)it is obtained some results for a polaron type model of the Pauli-Fierz model by means of a functional integral representation of a heat semigrounp. The result will be submitted somewhere as soon as possible.
For (3)an upper bound of the multiplicity of ground states of a Hamiltonian defined through a quadratic form, which is new as far as we know. It is submitted as the paper entitled
Multiplicity of ground states in quantum field models
We find that this method can be applied for a generalized spin-boson model.
A result concerning (4)is obtained for the so-called O(N)-spin model, and now we are writing a paper for this.
Throughout this project we can investigate a mass renormalization of the nonrelativistic QED, and we got some results contrary to a conventional physical claim, which is submitted as the paper entitled
Mass renormalization in nonrelativistic QED with spin 1/2 (with K.R.Ito)
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