The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled with classical nuclear dynamics, already known and studied both in quantum chemistry and in rigorous mathematical literature. We prove local existence of solutions for data in $$H^\sigma $$ H σ with $$\sigma \in [1,\frac{3}{2}[$$ σ ∈ [ 1 , 3 2 [ . In the course of the analysis a second new result of independent interest is discussed and proved, namely the construction of the propagator for the Dirac operator with several moving Coulomb singularities.

中文翻译：

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与点核动力学相互作用的狄拉克场

介绍并研究了描述与经典运动点核耦合的单​​个狄拉克电子场的系统。该模型是相应的与时间相关的单体 Hartree-Fock 方程与经典核动力学耦合的半相对论扩展，在量子化学和严格的数学文献中已经知道和研究。我们证明 $$H^\sigma $$ H σ 中数据的局部存在性，其中 $$\sigma \in [1,\frac{3}{2}[$$ σ ∈ [ 1 , 3 2 [ . 在分析过程中，讨论并证明了第二个独立感兴趣的新结果，即具有多个移动库仑奇点的狄拉克算子的传播子的构造。