量子化辐射耦合物质的解析微扰理论和重整化分析
Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation
摘要：
对于一大类物质和辐射的量子力学模型，我们发展了非简并基态的解析微扰理论。这个理论是适用的，例如，模型的物质与静态的核和非相对论性的电子耦合到紫外截止量子辐射场的偶极近似。如果能谱的最低点是哈密顿量的非简并本征值，我们表明，这个本征值是一个解析函数的核坐标和$α^{3/2}$，$α$是精细结构常数。一个适当选择的基态矢量解析地依赖于$α^{3/2}$，并且它相对于核坐标是连续可微分的。
英文摘要：
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of $α^{3/2}$, $α$ being the fine structure constant. A suitably chosen ground state vector depends analytically on $α^{3/2}$ and it is twice continuously differentiable with respect to the nuclear coordinates.
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