AI 中文总结
本文基于有限系统的逆极限提出严格实现威尔逊重正化群的新框架，避免病理性问题，为处理非平凡不动点等难题开辟新路径。
AI 中文摘要
自肯尼斯·威尔逊提出其获诺贝尔奖的重正化群思想以来，已过去五十多年。在此期间，尽管多次尝试，尚无数学结果以令人满意的程度实现威尔逊的愿景。尽管迄今为止，源于重正化群框架的许多预测已被证明，但这些证明通常依赖于替代思想，并未覆盖威尔逊重正化群的完整预测能力。在严格实现重正化群变换过程中发现的病理性问题进一步降低了数学界对该主题的热情。本文提出了一种新颖框架，基于有限系统的逆极限，以严格的方式实现威尔逊的原始思想。通过这种方式，避免了这些病理性问题，从而为威尔逊重正化群获得了一个数学上健全的框架。这为处理严格重正化群理论中的一些现有问题（如非平凡不动点的存在性）开辟了一条全新路径。
英文摘要
It has been over fifty years since Kenneth Wilson had his Nobel-prize-winning ideas on the renormalization group. In this time frame, despite many attempts, no mathematical results have implemented Wilson's vision to a satisfactory degree. Although a number of predictions stemming from the renormalization group framework have been proven to date, these proofs usually rely on alternative ideas and do not cover the full predictive power of Wilson's renormalization group. The discovery of pathologies within rigorous implementations of renormalization group transformations have further reduced the enthusiasm of the mathematics community for this subject. This paper presents a novel framework to implement Wilson's original idea in a rigorous manner based on inverse limits of finite systems. Doing so, one avoids these pathologies and hence obtains a mathematically sound framework for Wilson's renormalization group. This opens up a completely new path to tackle some of the existing problems in rigorous renormalization group theory like the existence of non-trivial fixed points.
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