AI 中文总结
本文研究 Dirac-Coulomb 系统基态，在充分大的 $c$ 下证明了基态在平移、相位变换和旋量旋转下的唯一性，确定了线性化算子核，并给出了非相对论极限下的渐近展开。
AI 中文摘要
我们研究如下 Dirac-Coulomb 系统在约束 $\norm[L^2]{u_c}^2=1$ 下的基态：$$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=\omega_cu_c.$$ 对于充分大的 $c$，我们证明了基态在平移、相位变换和旋量旋转下的唯一性，并确定了基态处线性化算子的核。我们还获得了非相对论极限区域中基态的渐近展开。
英文摘要
We study ground states of the following Dirac-Coulomb system $$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=ω_cu_c,$$ under the constraint $\norm[L^2]{u_c}^2=1.$For sufficiently large \(c\), we prove uniqueness of ground states modulo translations, phase transformations and spinorial rotations, and determine the kernel of the linearized operator at ground state. We also obtain asymptotic expansions of ground state in the nonrelativistic limit regime.
