We analyse the Casimir effect of two nonsingular centers of interaction in three space dimensions, using the framework developed by Herdegen. Our model is mathematically well-defined and all physical quantities are finite. We also consider a scaling limit, in which the problem tends to that with two Dirac \(\delta \)’s. In this limit the global Casimir energy diverges, but we obtain its asymptotic expansion, which turns out to be model dependent. On the other hand, outside singular supports of \(\delta \)’s the limit of energy density is a finite universal function (independent of the details of the nonsingular model before scaling). These facts confirm the conclusions obtained earlier for other systems within the approach adopted here: the form of the global Casimir force is usually dominated by the modification of the quantum state in the vicinity of macroscopic bodies.

我们使用Herdegen开发的框架，分析了三个空间维度上两个非奇异相互作用中心的卡西米尔效应。我们的模型在数学上定义明确，并且所有物理量都是有限的。我们还考虑了缩放限制，其中问题趋向于使用两个Dirac \（\ delta \）。在此极限下，整体卡西米尔能量发散，但我们得到了它的渐近扩展，事实证明这与模型有关。另一方面，\（\ delta \）的外部奇异支撑能量密度的极限是有限的通用函数（与缩放前非奇异模型的细节无关）。这些事实证实了先前在此处采用的方法中其他系统获得的结论：整体卡西米尔力的形式通常由宏观物体附近的量子态的改变所决定。