截止模型中的表面真空能：压力反常和分布引力极限
Surface Vacuum Energy in Cutoff Models: Pressure Anomaly and Distributional Gravitational Limit
摘要：
用理想反射边界进行的能量计算受到边界发散的困扰，这可能对应于边界附近发生的真实（但有限）物理效应。我们的工作假设是，应力张量的理想化边界条件与一些有限的截止应该是一个合理的特设模型的真实情况。当截断被去掉时，理论将有一个合理的重整化极限;这需要理解具有分布源的爱因斯坦方程。标准紫外截止的计算揭示了能量和压力之间的不一致性，类似于宇宙真空能量的非协变正则化。然而，如果截断是在平行于边界的“中性”方向上的空间点分离，则问题消失。在这里，我们证明这些索赔的细节，首先是一个单一的平面反射墙包围的测试边界，然后更严格的区域有限的截面包围的四个反射墙。我们还展示了如何的时刻膨胀定理可以应用到源的分布限制和爱因斯坦方程的解决方案，从而在数学上一致的微分方程，截止依赖系数已被确定为边界的属性的重正化。围绕这些结果的解释提出了一些问题。
英文摘要：
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor for idealized boundary conditions with some finite cutoff should be a reasonable ad hoc model for the true situation. The theory will have a sensible renormalized limit when the cutoff is taken away; this requires making sense of the Einstein equation with a distributional source. Calculations with the standard ultraviolet cutoff reveal an inconsistency between energy and pressure similar to the one that arises in noncovariant regularizations of cosmological vacuum energy. The problem disappears, however, if the cutoff is a spatial point separation in a "neutral" direction parallel to the boundary. Here we demonstrate these claims in detail, first for a single flat reflecting wall intersected by a test boundary, then more rigorously for a region of finite cross section surrounded by four reflecting walls. We also show how the moment-expansion theorem can be applied to the distributional limits of the source and the solution of the Einstein equation, resulting in a mathematically consistent differential equation where cutoff-dependent coefficients have been identified as renormalizations of properties of the boundary. A number of issues surrounding the interpretation of these results are aired.
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