| 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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| 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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