Complex velocity transformations and the Bisognano--Wichmann theorem for quantum fields acting on Krein spaces

非幺正Wightman conformal场论的Bisognano-Wichmann性质

The Bisognano-Wichmann property for non-unitary Wightman conformal field theories

本文研究非幺正Wightman场论中Bisognano-Wichmann性质的适用性，并通过Wightman公理推导出相关结果，证明了Haag双重要性。

正交的欧拉元素II：几何的比斯甘诺-维希曼定理和自旋-统计定理

Orthogonal pairs of Euler elements II: Geometric Bisognano--Wichmann and Spin--Statistics Theorems

本文在代数量子场论框架中研究正交欧拉元素，推导了比斯甘诺-维希曼定理和自旋-统计定理，揭示了其在楔形局部化中的几何结构。

The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole

Recent applications of Operator Algebras to Quantum Field Theory on a Curved Spacetime show that the incremental entropy associated with a quantum black hole, due the addition of a short range charge, is quantized proportionally to the logarithm of an integer. This talk first reviews the case of a Rindler black hole and then sketches the case of a spacetime with bifurcate Killing horizon and charges localizable on the horizon. An important tool is the construction of the conformal symmetries on the horizon.

从局部网到Euler元

From local nets to Euler elements

该研究在含Euler元的一般李群框架下，证明广义AQFT中几何实现模群由Euler元生成，且相关条件下正则性、可局部化性成立，楔形区域von Neumann代数为III_1型因子。

Algebraic Quantum Field Theory and Causal Symmetric Spaces

In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann algebras,we focus on Euler elements of the Lie algebra, i.e., elements whose adjoint action defines a 3-grading. We study the wedge regions they determine in corresponding causal symmetric spaces and describe some methods to construct nets of von Neumann algebras on causal symmetric spaces that satisfy abstract versions of the Reeh--Schlieder and the Bisognano-Wic…

Modular theory for the von Neumann algebras of Local Quantum Physics

In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an illustration of the Bisognano-Wichmann theorem for Wightman fields and in the algebraic setting, with a discussion on the physical meaning of this result. In the third part some reconstruction theorems based on modular groups will be described, in particular the possibility of constructing an action of the symmetry group of a given theory via modular groups, and the…

算子代数与量子场论讲义

Lecture Notes on Operator Algebras and Quantum Field Theory

本讲义为 EMS-IAMP 春季学校准备，在算子代数框架内介绍量子场论的当代概念与方法，涵盖模理论、局部协变性及黑洞视界附近量子场的热力学应用。

模理论与相对论标量量子场论中的贝尔-CHSH不等式

Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory

本文利用Tomita-Takesaki模理论探讨相对论标量量子场论中楔形区域的贝尔-CHSH不等式，通过构造楔形局部化的向量集，分析不同贝尔算符选择下不等式可能被违反的情况，并探讨实现Tsirelson界饱和的可能路径。

Wedge domains in compactly causal symmetric spaces

Motivated by construction in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces M=G/H, which includes in particular anti de Sitter space in all dimensions and its coverings. Our wedge domains generalize Rindler wedges in Minkowski space. The key geometric structure we use is the modular flow on M defined by an Euler element in the Lie algebra of G. Our main geometric result asserts that three seemingly different characterizations of these domains coincide: the positivity domain of the modular vector field; the domain specified by a KMS like analytic …

有限精度代数量子场论

Finite-Precision Algebraic Quantum Field Theory: Quantum Parcels, Locality, Modular Structure and Factors

研究将区间量子力学方法扩展到代数量子场论，提出区间代数量子场论，通过开发包约简等方法，重新表述AQFT主要结构特征，证明有限精度下相关特性仍存在，还恢复了因子分类等，提供了相对论量子理论的有限精度统一表述。