论文标题
Maxwell-Pauli方程
The Maxwell-Pauli Equations
论文作者
论文摘要
我们研究了$ n \ geq 1 $非权利性电子的量子机械多体问题，并与自旋相互作用的自发性经典电磁场和$ k \ geq 0 $ static nuclei相互作用。我们使用所谓的多体Maxwell-Pauli方程对电子的动力学及其自我生成的电磁场进行建模。本论文的主要结果是在假设良好的结构常数$α$和核电荷的假设下，构建了多体麦克斯韦 - 波利语方程的时间全球，有限能源的弱解决方案。关于$α$和核电的大小的假设可确保我们对该系统具有能量稳定性，即，绝对基态能量存在。本文中的工作是理解量子力学中物质稳定性与相应动力学方程的良好性之间的连接的第一步。
We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons and their self-generated electromagnetic field using the so-called many-body Maxwell-Pauli equations. The main result of this thesis is to construct time global, finite-energy, weak solutions to the many-body Maxwell-Pauli equations under the assumption that the fine structure constant $α$ and the nuclear charges are not too large. The assumptions on the size of $α$ and the nuclear charges ensure that we have energetic stability for this system, i.e., the absolute ground state energy exists. The work in this thesis serves as an initial step towards understanding the connection between the energetic stability of matter in quantum mechanics and the well-posedness of the corresponding dynamical equations.
