Extension of the structure theorem of Borchers and its application to half-sided modular inclusions

半边模包含的相对位置

Relative Positions of Half-sided Modular Inclusions

本文研究公共标准子空间中两个半边模包含的相对位置，证明其包含关系等价于对应正单参数群生成元的谱子空间包含，给出算子值对称内函数的刻画并辅以非平凡现象示例。

Deformations of half-sided modular inclusions and non-local chiral field theories

We construct explicit examples of half-sided modular inclusions ${\mathcal N}\subset{\mathcal M}$ of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms of an algebra localized at infinity, we consider a second quantization inclusion ${\mathcal N}\subset{\mathcal M}$ with large relative commutant and construct a one-parameter family ${\mathcal N}_κ\subset{\mathcal M}_κ$, $κ\geq0$, of half-sided inclusions such that ${\mathcal N}_0={\mathcal N}$, ${\mathcal M}_0={\mathcal M}$ and ${\mathcal N}_κ'\cap{\mathcal…

The Relative Weak Asymptotic Homomorphism Property for Inclusions of Finite von Neumann Algebras

A triple of finite von Neumann algebras $B\subseteq N\subseteq M$ is said to have the relative weak asymptotic homomorphism property if there exists a net of unitary operators $\{u_λ\}_{λ\in Λ}$ in $B$ such that $$\lim_λ|\mathbb{E}}_B(xu_λy)-{\mathbb{E}}_B({\mathbb{E}}_N(x)u_λ{\mathbb{E}}_N(y))\|_2=0$$ for all $x,y\in M$. We prove that a triple of finite von Neumann algebras $B\subseteq N\subseteq M$ has the relative weak asymptotic homomorphism property if and only if $N$ contains the set of all $x\in M$ such that $Bx\subseteq \sum_{i=1}^n x_iB$ for a finite number of elements $x_1,...,x_n$ i…

扭曲 Araki-Woods 代数的模结构与包含关系

Modular Structure and Inclusions of Twisted Araki-Woods Algebras

本文分析了扭曲 Araki-Woods 代数的模结构与包含关系，证明了 Fock 真空循环分离的条件并显式确定了 Tomita-Takesaki 模数据，同时探讨了包含关系的奇异性与 III 型相对交换子，最后应用于代数量子场论中的可观测量的定域化。

相对熵与弯曲时空

Relative entropy and curved spacetimes

本文证明了标准子空间半侧模包含下熵函数的凸性，并将其应用于稳态弯曲时空上自由量子场论中相干态的 QNEC 不等式研究。

Structure for Regular Inclusions

We study pairs (C,D) of unital C*-algebras where D is a regular abelian C*-subalgebra of C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D whose restriction to D is the identity on D. We show that the left kernel of E, L(C,D), is the unique closed two-sided ideal of C maximal with respect to having trivial intersection with D. When L(C,D)=0, we show the MASA D norms C. We apply these results to extend existing results in the literature on isometric isomorphisms of norm-closed subalgebras which lie be…