论文标题
代数量子场理论的空间类别和偏见
Spacetimes categories and disjointness for algebraic quantum field theory
论文作者
论文摘要
代数量子场理论（AQFT）可以以从一类空间到可观察的代数类别的函数表示。但是，一个通用类别$ \ mathsf {c} $，其对象将解释为空间不一定是AQFT函数的域而言不一定可行。通常，必须强加对$ \ mathsf {c} $的形态的其他约束。我们引入了偏见关系，贝尼尼，申克尔和沃克的正交关系的概括（Arxiv：1709.08657）。在任何类别中，$ \ MATHSF {C} $配备了不相关关系，我们确定一个子类别$ \ Mathsf {d} _ \ Mathsf {C} $，可作为AQFT的域。我们验证时，当$ \ mathsf {c} $是所有全球双曲平台的类别时，维度$ d+1 $和所有局部异构体，配备了空间分离的差异关系，指定的子类别$ \ mathsf {d} _ \ mathsf {c c} comain ins commut $ \ mathsf {loc} _ {d+1} $ of perativistic aqfts。通过识别适当的手性偏见关系，我们构建了一个类别$χ\ Mathsf {loc} $，适合在两个维度中作为手性结合域理论（CFTS）的域。我们将其与既定的手性CFT的AQFT公式进行了比较，并表明在已建立的配方中表达的任何手性CFT诱导了一个在$χ\ \ Mathsf {loc} $上定义的手性CFT。
An algebraic quantum field theory (AQFT) may be expressed as a functor from a category of spacetimes to a category of algebras of observables. However, a generic category $\mathsf{C}$ whose objects admit interpretation as spacetimes is not necessarily viable as the domain of an AQFT functor; often, additional constraints on the morphisms of $\mathsf{C}$ must be imposed. We introduce disjointness relations, a generalisation of the orthogonality relations of Benini, Schenkel and Woike (arXiv:1709.08657). In any category $\mathsf{C}$ equipped with a disjointness relation, we identify a subcategory $\mathsf{D}_\mathsf{C}$ which is suitable as the domain of an AQFT. We verify that when $\mathsf{C}$ is the category of all globally hyperbolic spacetimes of dimension $d+1$ and all local isometries, equipped with the disjointness relation of spacelike separation, the specified subcategory $\mathsf{D}_\mathsf{C}$ is the commonly-used domain $\mathsf{Loc}_{d+1}$ of relativistic AQFTs. By identifying appropriate chiral disjointness relations, we construct a category $χ\mathsf{Loc}$ suitable as domain for chiral conformal field theories (CFTs) in two dimensions. We compare this to an established AQFT formulation of chiral CFTs, and show that any chiral CFT expressed in the established formulation induces one defined on $χ\mathsf{Loc}$.
