标题： 红外渐近行为 显示英文标题

标题： Asymptotics of the Infrared

摘要： 我们借鉴量子场论中维度约化环路算符的最新表述以及概率格点动力学的精确表示，提出了一种新的划分函数零点评估方案，从而能够对量子临界现象进行显式分析。 这种新方法通过分解的量子环算子基底获得划分函数零点，并且，正如我们所展示的，它构成了一种有效的映射，将重整化群的 $\beta$ 函数映射到可数有限希尔伯特空间的非交换局域算子基底上。 按照近期的研究处理方式，讨论了 CP 破坏的 Vafa-Witten 定理及相关欧几里得场论的复作用量问题，并证明这些问题是这些零点极限分布解析性以及红外区域重整化群方程不动点附近主导量子涨落支配的真空态性质的自然结果。 显示英文摘要

摘要： We follow recent formulations of dimensionally reduced loop operators for quantum field theories and exact representations of probabilistic lattice dynamics to identify a new scheme for the evaluation of partition function zeroes, allowing for the explicit analysis of quantum critical phenomena. This new approach gives partition function zeroes from a factored quantum loop operator basis and, as we show, constitutes an effective mapping of the renormalization group $\beta$-function onto the noncommuting local operator basis of a countably finite Hilbert space. The Vafa-Witten theorem for CP-violation and related complex action problems of Euclidean Field theories are discussed, following recent treatments, and are shown to be natural consequences of the analyticity of the limiting distribution of these zeroes, and properties of vacuum regimes governed by a dominant quantum fluctuation in the vicinity of a renormalization group equation fixed point in the infrared.