Mathematical problems in quantum field theory and infinite dimensional analysis
| Project/Area Number |
15K04888
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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, 理学研究院, 特任教授 (80134807)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | フォック空間 / 無限次元解析 / 無限次元デイラック作用素 / 無限次元ラプラシアン / 超対称性 / 超対称的量子場 / 時間作用素 / 正準交換関係と正準反交換関係の表現 / 量子場 / 正準反交換関係 / 基底状態 / 正準交換関係 / 量子ディラック場 / 無限次元ディラック作用素 / 縮退度 / ハミルトニアン / ディラック場 / スカラー場 |
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| Outline of Final Research Achievements |
(1) An upper bound for the multiplicity of ground state of a class of quantum field models has been derived. (2) Detailed analyses have been done on in-equivalent representations of canonical commutation relations and canonical anti-commutation relations, which have physically important meanings. (3) For a general quantum system, a concept of ultra-weak time-operator has been introduced. Hierarchies of time-operators and their respective physical roles have been considered.
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Report
(4 results)
Research Products
(13 results)
