发表机构
National Research and Innovation Agency (BRIN); Institut Teknologi Bandung; University of Science and Technology of China（国家研究与创新署; 万隆理工学院; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究Christ--Lee扭结的涨落谱与单圈量子质量，通过精确约化为Heun方程获得阈值与谱层级，揭示小形变下对数修正，统一描述谱重组对半经典量子质量的控制。
AI 中文摘要
我们研究了Christ--Lee扭结在其形变参数全部正值范围内的涨落谱和重整化单圈量子质量。涨落方程被精确约化为一般Heun形式，从而得到宇称分辨的连续谱解和离散谱的隐式量子化条件。在第一个非平凡连续谱交叉处，奇Heun解截断为多项式，给出精确阈值\\(\epsilon_1=\sqrt{\sqrt{3}-1}\\)。在小形变极限下，扭结分离为两个间距很大的\\(\phi^6\\)型界面，涨落算符发展出一个长的中央空腔。该几何结构解释了束缚态数目的对数增长、连续谱阈值交叉的渐近几何层级以及软相对平移模的出现。在相反的极限下，谱趋近于\\(\phi^4\\) Pöschl--Teller问题，而其偶阈值共振在有限形变下变为浅束缚态。单圈修正采用固定真空正规排序方案，通过公共正则子谱迹独立地通过虚频泛函行列式进行评估。两种计算在代表性有限形变下一致，并精确复现\\(\phi^4\\)极限。在小形变区域，延长的中央区域产生对数增强的负量子修正。这些结果提供了统一的分析和数值描述，说明Christ--Lee扭结的谱重组如何控制其半经典量子质量。
英文摘要
We study the fluctuation spectrum and renormalized one-loop quantum mass of the Christ--Lee kink over the full positive range of its deformation parameter. The fluctuation equation is reduced exactly to general-Heun form, yielding parity-resolved continuum solutions and implicit quantization conditions for the discrete spectrum. At the first nontrivial continuum crossing, the odd Heun solution truncates to a polynomial, giving the exact threshold \(ε_1=\sqrt{\sqrt{3}-1}\). For small deformation, the kink separates into two widely spaced \(ϕ^6\)-like interfaces and the fluctuation operator develops a long central cavity. This geometry explains the logarithmic growth of the bound-state count, the asymptotically geometric hierarchy of continuum-threshold crossings, and the emergence of a soft relative-translation mode. In the opposite limit, the spectrum approaches the \(ϕ^4\) Pöschl--Teller problem, while its even threshold resonance becomes a shallow bound state at finite deformation. The one-loop correction is evaluated in a fixed vacuum-normal-ordering prescription using a common-regulator spectral trace and independently through an imaginary-frequency functional determinant. The two calculations agree throughout representative finite deformations and reproduce the exact \(ϕ^4\) limit. In the small-deformation regime, the extended central region produces a logarithmically enhanced negative quantum correction. These results provide a unified analytic and numerical description of how the spectral reorganization of the Christ--Lee kink controls its semiclassical quantum mass.
