论文标题
平滑的一维代数量子场理论
Smooth 1-dimensional algebraic quantum field theories
论文作者
论文摘要
本文提出了对代数量子场理论（AQFTS）通常的概念的改进，从而使这些理论平稳，从某种意义上说，它们分配给了每个平稳的空间家族，一个平稳的可观察代数家族。使用一堆类别，该提案是为了最简单的一维空间而具体实现的，从而导致一堆平滑的一维AQFTS。构建了光滑的AQFT，光滑AQFT的光滑家族的具体示例和均衡的光滑AQFT。确定并讨论了将这种方法升级到更高维度和衡量理论的主要开放问题。
This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using stacks of categories, this proposal is realized concretely for the simplest case of 1-dimensional spacetimes, leading to a stack of smooth 1-dimensional AQFTs. Concrete examples of smooth AQFTs, of smooth families of smooth AQFTs and of equivariant smooth AQFTs are constructed. The main open problems that arise in upgrading this approach to higher dimensions and gauge theories are identified and discussed.
