真空能计算与热核系数关系的系统化
Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
摘要：
卡西米尔能量是一种非局部效应;它的大小不能从热核展开式中推导出来，即使是那些包括积分边界项的展开式。另一方面，已知正则化（但尚未重整化）的总真空能量中的发散项与热核系数相关联。在这里，最近的研究之间的关系的本征值密度，热核，和积分核的运营商$e^{-t\sqrt{H}}$被利用来完全描述这种关联。关于正则化能量结构的各种先前孤立的观察自然出现。20多年来，争论一直存在，源于这样一个事实，即腔内部重整化真空能量密度中的某些（可能是物理上有意义的）项在边界处变得奇异，并与正则化总能量中的某些发散项相关。本文的观点有望帮助解决这些问题。
英文摘要：
Casimir energy is a nonlocal effect; its magnitude cannot be deduced from heat kernel expansions, even those including the integrated boundary terms. On the other hand, it is known that the divergent terms in the regularized (but not yet renormalized) total vacuum energy are associated with the heat kernel coefficients. Here a recent study of the relations among the eigenvalue density, the heat kernel, and the integral kernel of the operator $e^{-t\sqrt{H}}$ is exploited to characterize this association completely. Various previously isolated observations about the structure of the regularized energy emerge naturally. For over 20 years controversies have persisted stemming from the fact that certain (presumably physically meaningful) terms in the renormalized vacuum energy density in the interior of a cavity become singular at the boundary and correlate to certain divergent terms in the regularized total energy. The point of view of the present paper promises to help resolve these issues.
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