标题： 狄拉克极化子的谱分析 显示英文标题

标题： Spectral Analysis of the Dirac Polaron

摘要： 考虑一个狄拉克粒子与辐射场相互作用的系统。 系统的哈密顿量由$H = \alpha\cdot(\hat\mathbf{p}-q\mathbf{A}(\hat\mathbf{x}))+m\beta + H_f$定义，其中 $q\in\mathbb{R}$是耦合常数，$\mathbf{A}(\hat\mathbf{x})$表示量子化的矢量势，$H_f$表示自由光子哈密顿量。 由于总动量是守恒的，$H$按总动量分解，纤维哈密顿量为$H(\mathbf{p}), (\mathbf{p}\in\mathbb{R}^3)$。 由于自伴算子$H(\mathbf{p})$从下方有界，可以定义最低能量$E(\mathbf{p},m):=\inf\sigma(H(\mathbf{p}))$。我们证明在以下条件下$E(\mathbf{p},m)$是$H(\mathbf{p})$的本征值：(i) 红外正则化和 (ii)$E(\mathbf{p},m)<E(\mathbf{p},0)$。我们还讨论了极化矢量和角动量。 显示英文摘要

摘要： A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by $H = \alpha\cdot(\hat\mathbf{p}-q\mathbf{A}(\hat\mathbf{x}))+m\beta + H_f$ where $q\in\mathbb{R}$ is a coupling constant, $\mathbf{A}(\hat\mathbf{x})$ denotes the quantized vector potential and $H_f$ denotes the free photon Hamiltonian. Since the total momentum is conserved, $H$ is decomposed with respect to the total momentum with fiber Hamiltonian $H(\mathbf{p}), (\mathbf{p}\in\mathbb{R}^3)$. Since the self-adjoint operator $H(\mathbf{p})$ is bounded from below, one can define the lowest energy $E(\mathbf{p},m):=\inf\sigma(H(\mathbf{p}))$. We prove that $E(\mathbf{p},m)$ is an eigenvalue of $H(\mathbf{p})$ under the following conditions: (i) infrared regularization and (ii) $E(\mathbf{p},m)<E(\mathbf{p},0)$. We also discuss the polarization vectors and the angular momenta.