AI 中文总结
该研究分析了 Gribov 视界与 Zwanziger 视界函数的逐构型关系，针对三维、四维欧几里得空间的径向 SU(2) 刺猬背景，用变分估计等方法研究了相关谱方向的可访问性等问题。
AI 中文摘要
我们研究了由 Faddeev-Popov 算子失去正定性定义的第一 Gribov 视界，与通过依赖背景的源探测逆算子的 Zwanziger 视界函数之间逐构型的关系。分析聚焦于 Gribov 视界 onset 相关的谱方向是否必然可被视界函数包含的源访问，包括临界子空间退化的情形。针对三维和四维欧几里得空间中的径向 SU(2) 刺猬背景研究该问题，其中角对称性约束源区，而径向轮廓控制 Faddeev-Popov 阈值的排序。采用变分估计和有限体积计算表征光滑径向轮廓的阈值结构。由于全空间设置中零能行为与视界源相关的区域问题，单独处理正则规范的 BPST 背景。讨论限于逐构型的谱性质，不涉及杨-米尔斯泛函积分中这些背景的统计权重。
英文摘要
We examine the configurationwise relation between the first Gribov horizon, defined by loss of positivity of the Faddeev-Popov operator, and Zwanziger's horizon function, which probes the inverse operator through background-dependent sources. The analysis focuses on whether the spectral directions associated with the onset of the Gribov horizon are necessarily accessible to the sources entering the horizon function, including situations in which the critical subspace is degenerate. This question is studied for radial SU(2) hedgehog backgrounds in three and four Euclidean dimensions, where angular symmetry constrains the source sector while the radial profile controls the ordering of Faddeev-Popov thresholds. Variational estimates and finite-volume calculations are used to characterize the threshold structure for smooth radial profiles. The regular-gauge BPST background is treated separately because of domain issues associated with zero-energy behavior and the horizon source in the full-space setting. The discussion is restricted to configurationwise spectral properties and does not address the statistical weighting of these backgrounds in the Yang-Mills functional integral.
