We evaluate the quantum expectation values in nonsimply connected spaces by using UV improved Green’s functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green’s functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.

中文翻译：

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三种UV在非平凡背景空间中的真空期望值改进了格林函数

我们通过使用 Padmanabhan、Abel 和 Siegel 提出的 UV 改进格林函数来评估非简单连接空间中的量子期望值。发现这三种格林函数的结果在尺度变化下表现相似，但有细微差别。简要讨论了进一步应用的前景。