Mathematical analysis on quantum fields
| Project/Area Number |
24540154
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
ARAI Asao 北海道大学, 理学(系)研究科(研究院), 教授 (80134807)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 漸近的摂動論 / 基底状態 / 量子場 / 無限次元ディラック作用素 / 汎関数積分 / フォック空間 / ハミルトニアン / スペクトル理論 / Dirac作用素 / Golden-Thompson不等式 / 正準交換関係 / 量子ゼノン効果 / 超対称性 / 分配関数 / ゴールデン・トンプソン不等式 / 量子電磁力学 / ディラック粒子 / ヒルベルト空間 / 摂動論 / スピン-ボソンモデル |
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| Outline of Final Research Achievements |
(1) A new asymptotic perturbation theory is constructed for a class of linear operators on a Hilbert space and applied to a model of mass-less quantum fields.
As a result, it is shown that the ground state energy of the model has an asymptotic expansion in the coupling constant up to any finite order. (2) A spectral analysis is made on a class of infinite dimensional Dirac operators Q on the abstract boson-fermion Fock space. In particular, it is shown that Q has non-zero eigenvalues in a strong coupling region independently of whether or not the unperturbed part of Q has a non-zero eigenvalue. (3) Functional integral representations are derived for a general class of boson-fermion systems with application to statistical mechanics.
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Report
(4 results)
Research Products
(16 results)
