Mathematical Analysis of Quantum Fields
| Project/Area Number |
21540158
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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 | Hokkaido University |
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Principal Investigator |
ARAI Asao 北海道大学, 大学院・理学研究院, 教授 (80134807)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 量子場 / 量子電磁力学 / ディラック作用素 / ハイゼンベルク作用素 / ディラック粒子 / 量子幅射場 / 時間作用素 / ハミルトニアン / 量子力学 / 量子保存量 / ラムシフト / リウヴィリアン / 代数的量子力学 / 量子輻射場 / チッターベヴェーグング |
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| Research Abstract |
A relativistic charged particle with spin 1/2 is called a Dirac particle and it interacts with the quantum radiation field. The quantum Hamiltonian which describes the interaction-the Dirac-Maxwell operator-was analyzed mathematically. For the time development of the position operator of the Dirac particle, an integral equation was derived and asymptotic formulae were established in the charge as an parameter. Related to this, radiative corrections to the Zitterbewegung of the Dirac particle was computed. One of the other important results was spectral analysis of an effective Hamiltonian in non-relativistic quantum electrodynamics, which is obtained as a non-relativistic limit of the Dirac-Maxwell operator, where a mathematically rigorous foundation was given to the Lamb shift in the hydrogen atom.
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Report
(4 results)
Research Products
(27 results)
