重整化群对Araki相对熵的界

中文摘要 AI 辅助

本文推导了一个多尺度Bakry-Émery准则，用于给出相对论量子场论中平衡态微扰的Araki相对熵的上界。利用随机正性，相对论玻色子场的关联微扰可以与有质量欧几里得自由场的微扰建立对应关系。这给出了一个Feynman-Kac公式，进而用于推导Araki相对熵的概率表达式。将有质量欧几里得自由场描述为抽象Wiener空间，提供了推导Polchinski方程的无穷维框架。将Bauerschmidt、Bodineau和Dagallier的方法扩展到这一情境，得到了Araki相对熵的概率界，该界可以完全用算子代数术语表述。利用该准则，证明了紫外有限区域中的洛伦兹有质量Sine-Gordon模型满足相对熵界。

英文摘要

This paper derives a multiscale Bakry-Émery criterion for an upper bound on the Araki relative entropy of perturbations of an equilibrium state in relativistic QFT. Using stochastic positivity, affiliated perturbations of the relativistic bosonic field can be put in correspondence with perturbations of the massive Euclidean free field. This gives a Feynman-Kac formula, which in turns is used to derive a probabilistic expression for the Araki relative entropy. The description of the massive Euclidean free field as an abstract Wiener space provides the infinite-dimensional framework to derive a Polchinski equation. Extending the methods of Bauerschmidt, Bodineau, and Dagallier to this context yields a probabilistic bound on the Araki relative entropy, which can be formulated entirely in operator-algebraic terms. Using the criterion, it is shown that the Lorentzian massive Sine-Gordon model in the ultraviolet finite regime satisfies the relative entropy bound.

发表机构

• Università di Milano（米兰大学）

机构由 AI 辅助整理，请以论文原文为准。