Mathematical Analysis of Quantum Fields

自旋为1/2的相对论带电粒子称为狄拉克粒子，它与量子辐射场相互作用。对描述相互作用的量子哈密顿量--狄拉克-麦克斯韦算符--进行了数学分析。对于狄拉克粒子位置算符随时间的发展，推导了以电荷为参数的积分方程解，并建立了渐近公式。与此相关，计算了狄拉克粒子的Zitterbewegung辐射修正。另一个重要的结果是非相对论量子电动力学中有效哈密顿量的谱分析，它是作为Dirac-Maxwell算符的非相对论极限得到的，其中氢原子的Lamb位移得到了严格的数学基础。

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.