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Coarse-graining of the Einstein–Hilbert action rewritten by the Fisher information metric
International Journal of Modern Physics A ( IF 1.6 ) Pub Date : 2020-09-22 , DOI: 10.1142/s0217751x20501572
Shingo Takeuchi 1
Affiliation  

In this study, considering the Fisher information metric (Fisher metric) given by a specific form, which is the form of weights in statistics, we rewrite the Einstein–Hilbert (EH) action. Then, determining the transformation rules of the Fisher metric, etc under the coarse-graining, we perform the coarse-graining toward that rewritten EH action. We finally show an existence of a trivial fixed-point. Here, the existence of a trivial fixed-point is not trivial for us because we consider the metric given by the Fisher metric, which is not the normal metric and has to satisfy some constraint in the formalism of the Fisher metric. We use the path-integral in our analysis. At this time we have to accept that a fundamental constraint in the formalism of the Fisher metric is broken at the quantum level. However we consider we can accept this with the thought that some constraints and causal relations held at the classical level usually get broken at the quantum level. We finds some problems of the Fisher metric. The space–time we consider in this study is two-dimensional.

中文翻译:

由费舍尔信息度量重写的爱因斯坦-希尔伯特动作的粗粒度

在本研究中,考虑到由特定形式给出的Fisher信息度量(Fisher metric),即统计学中的权重形式,我们重写了爱因斯坦-希尔伯特(EH)动作。然后,在粗粒度下确定 Fisher 度量等的转换规则,我们对重写的 EH 动作执行粗粒度。我们最终证明了一个平凡不动点的存在。在这里,平凡不动点的存在对我们来说不是微不足道的,因为我们考虑由 Fisher 度量给出的度量,它不是正常的度量,并且必须满足 Fisher 度量形式的一些约束。我们在分析中使用路径积分。此时,我们必须接受,Fisher 度量的形式主义中的一个基本约束在量子水平上被打破了。然而,我们认为我们可以接受这一点,认为经典水平上的一些约束和因果关系通常在量子水平上被打破。我们发现了 Fisher 度量的一些问题。我们在本研究中考虑的时空是二维的。
更新日期:2020-09-22
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