发表机构
Rikkyo University; RIKEN; Kanazawa University（立教大学; 理化学研究所; 金泽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将Wilson重整化群视为量子信道，并发展代数扩展与资源理论，引入相对熵单调量及紫外信息度量，揭示其与中心荷差及全息实现的关联。
AI 中文摘要
重整化群（RG）是物理学中从统计力学到量子场论的核心概念，然而其方案在场论与多体物理之间差异显著。我们将Wilson重整化群表述为量子信道，其Kraus表示对纯输入产生纯条件轨迹，并在平均后恢复混合态流。随后，我们发展了一种代数扩展，适用于超越通常动量空间因子化设定：低能代数由单粒子谱构造，粗粒化是其上的条件期望。我们进一步构建了RG的资源理论，其中自由态为不动点。在所述假设下，所得相对熵单调量在二维红外不动点附近沿单一稳定RG方向，与$c-c_{\ m IR}$成二次阶比例。我们还引入了一种互补度量，用于衡量粗粒化所丢弃的紫外信息，建立了其在连续粗粒化映射下的单调性，并讨论了其全息实现。
英文摘要
Renormalization group (RG) is a core concept in physics from statistical mechanics to quantum field theory, yet its schemes differ widely between field theory and many-body physics. We formulate the Wilsonian RG as a quantum channel, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension applicable beyond the usual momentum-space, factorized setting: the low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. We further construct a resource theory of RG whose free states are fixed points. For thermal states, the resulting relative-entropy monotone is proportional to $c-c_{\rm IR}$ to quadratic order along a single stable RG direction near a two-dimensional IR fixed point. We also introduce a complementary measure of the UV information discarded by coarse graining, establish its monotonicity for successive coarse-graining maps, and discuss its holographic realization.
Comments11 pages, 2 figures (v1); clarified notations and assumptions (v2)
