2011 Fiscal Year Final Research Report
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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| 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 |
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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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