AI 中文总结
该研究在带孔闵可夫斯基时空中引入Robin边界条件，推导边界诱导的Wightman函数，分析其对Unruh-DeWitt探测器响应的修正，发现边界贡献可增强或抑制响应且无相互作用时长线性项。
AI 中文摘要
我们研究带孔闵可夫斯基时空中的实无质量标量场，该场在被移除的原点处满足稳定的单参数Robin边界条件$G(0)-\beta G'(0)=0$（其中$\beta\geq0$）。我们以闭式形式得到了静态基态Wightman函数中由边界诱导的部分，并研究了匀速加速的Unruh-DeWitt探测器的响应。该破缺了稳定Unruh响应所基于的洛伦兹 boost对称性，因此边界诱导的 pullback在固有时中是非平稳的。对应的扣除探测器贡献既可以增强也可以抑制普通闵可夫斯基响应，且依赖于Robin参数、能隙以及轨迹的采样部分。对于详细研究的未偏移径向对齐轨迹，我们证明边界诱导的pullback在两个固有时变量中是绝对可积的。因此，当光滑相互作用扩展到探测器的整个历史时，该贡献趋近于有限极限且保持为$O(1)$，不会产生与相互作用时长线性相关的额外项。形式上的Neumann极限是奇异的：由于s波扇区中的红外奇点，边界诱导的两点函数呈对数增长，数值响应表现出与该渐近行为一致的增长。
英文摘要
We consider a real massless scalar field in punctured Minkowski spacetime, endowed at the removed origin with the stable one-parameter family of Robin boundary conditions $G(0)-βG'(0)=0$, $β\geq0$. We obtain the boundary-induced part of the static ground-state Wightman function in closed form and study the response of a uniformly accelerated Unruh-DeWitt detector. The puncture breaks the boost symmetry underlying the stationary Unruh response, so the boundary-induced pullback is nonstationary in proper time. The corresponding subtracted detector contribution can either enhance or suppress the ordinary Minkowski response and depends on the Robin parameter, the detector gap, and the portion of the trajectory sampled. For the unshifted, radially aligned trajectory studied in detail, we prove that the boundary-induced pullback is absolutely integrable in the two proper-time variables. Consequently, as the smooth interaction is extended over the full detector history, this contribution approaches a finite limit and remains $O(1)$, producing no additional term linear in the interaction duration. The formal Neumann limit is singular: the boundary-induced two-point function grows logarithmically because of an infrared singularity in the $s$-wave sector, and the numerical response exhibits growth consistent with this asymptotic behavior.
Comments8 pages, 5 figures, accepted for publication in Phys. Rev. D
