Gribov-Zwanziger理论中的Casimir效应
The Casimir effect in Gribov-Zwanziger theory
- KU Leuven Campus Kortrijk-Kulak（荷语鲁汶大学科特赖克-库拉克校区）
- CBPF − - Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）
- Ghent University（根特大学）
- Institute of Research and Development, Duy Tan University（育达大学研发院）
- Faculty of Natural Sciences, Duy Tan University（育达大学自然科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究Gribov-Zwanziger理论中平行板边界下的Casimir效应，利用泛函积分方法计算PMC和PEC板的Casimir能量，并与格点数据比较，发现Gribov质量不依赖于板间距。
AI中文摘要：
我们考虑具有两块无限大平行板的Yang-Mills理论，两板间距为\\(L\\)，板为理想磁导体（PMC）或理想电导体（PEC）。近期研究表明，在此设置中Gribov副本问题仍然存在。我们随后利用泛函积分方法研究存在这些边界时的Gribov-Zwanziger（GZ）作用量。拉格朗日乘子场允许将边界条件提升到作用量中，之后可以直接确定对胶子传播子的边界修正。在PEC情形下，我们提供证据表明，即使平移不变性（部分）被破坏，GZ作用量中通常的视界项仍将泛函积分限制在Gribov区域。我们针对具有PMC或PEC板的GZ理论计算了Casimir能量，既直接从泛函积分计算，也从能量-动量张量计算，得到一致的结果。我们将解析结果与近期格点数据在4D和3D中进行比较。先验地，人们可能预期边界修正的胶子传播子会在GZ间隙方程中引入新的\\(L\\)依赖性。这将使Gribov质量\\(\gamma\\)动态依赖于\\(L\\)，从而与Casimir能量产生有趣的相互作用。然而，我们表明在当前近似下不会出现这种动态的\\(L\\)依赖性。
英文摘要：
We consider Yang-Mills theory with two infinite parallel plates, separated by a distance \(L\), that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new \(L\)-dependencies into the GZ gap equation. This would make the Gribov mass \(γ\) dynamically dependent on \(L\), implying an interesting interplay with the Casimir energy. However, we show that no such dynamical \(L\)-dependence occurs within the current approximation.
