关于实用模和正则化方法的注记：宇宙学背景下的量子分裂
Note on the pragmatic mode-sum regularization method: translational-splitting in a cosmological background
摘要：
点分裂重整化方法提供了一种计算一般弯曲时空中量子场二次算符有限期望值的方法。Levi和Ori最近证明，当背景度规具有等距性时，如静止或球对称黑洞，该方法可以升级为一种实用的重整化过程，产生有效的数值计算。在这份说明中，我们表明，当背景享有三维空间对称性，如均匀膨胀的宇宙，上述实用的正则化技术减少到完善的绝热正则化方法。
英文摘要：
The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization method.
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