通过统计推断的重正化组
The renormalisation group via statistical inference
摘要：
在物理学中，人们试图根据不完全测量的结果来推断控制系统的规则。因此，微观理论在实验上可能是无法有效区分的。我们开发了一个操作动机的程序，以确定相应的等价类的状态，并认为重正化组产生的固有的模糊性与类：一个遇到流参数，例如，一个调节器，一个尺度，或一个精确度的测量，它指定了一个给定的等价类中的代表。这提供了一个统一的框架，并确定了信息在重新正常化中所发挥的作用。我们验证了这一想法表明，它证明了使用低动量n点函数作为统计相关的观测值周围的高斯假设。这些结果使得在量子场论中计算量子化能力成为可能。我们的方法还提供了一种方法来扩展重正化技术的有效模型，这不是基于通常的量子场形式主义，并阐明了各种类型的RG之间的关系。
英文摘要：
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalisation group arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and identifies the role played by information in renormalisation. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalisation techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.
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