标题： 相对论量子电动力学中固定总动量模型的基态 显示英文标题

标题： Ground State of a Model in Relativistic Quantum Electrodynamics with a Fixed Total Momentum

摘要： 一个考虑单个相对论性电子与量子化电磁场相互作用的系统。 我们主要研究总动量固定的系统$\mathbf{p}$ —— 该系统称为狄拉克极化子。 我们分析狄拉克极化子的最低能量$E(\mathbf{p})$，并推导出一些性质：凹性、对称性和逆能不等式$E(\mathbf{p})\leq E(0)$，$\mathbf{p}\in\mathbb{R}^3$。 此外，我们考虑狄拉克极化子模型基态的存在性。 我们证明，在包含红外正则化条件和紫外截断条件的条件下，狄拉克极化子模型存在基态。 这确保了相对论性“穿衣”单电子态的存在。 显示英文摘要

摘要： A system of a single relativistic electron interacting with the quantized electromagnetic field is considered. We mainly study this system with a fixed total momentum $\mathbf{p}$ -- This system is called the Dirac polaron. We analyze the lowest energy $E(\mathbf{p})$ of the Dirac polaron, and derive some properties: concavity, symmetricity, and the inverse energy inequality $E(\mathbf{p})\leq E(0)$, $\mathbf{p}\in\mathbb{R}^3$. Furthermore, we consider the existence of the ground state of the Dirac polaron model. We show that the Dirac polaron model has a ground state under a condition which includes an infrared regularization condition and an ultraviolet cutoff. This ensures that the relativistic dressed one electron state exists.