论文标题
量子场的功能演变
Functorial evolution of quantum fields
论文作者
论文摘要
我们提出了一个组成代数框架，以在离散的空间中描述量子场的演变。我们展示了相对论和量子因果关系中熟悉的概念如何以纯粹的理论方式从时空事件的因果关系顺序中恢复，而没有直接提及分析或拓扑。我们以组成的功能方式制定了因果秩序与因果秩序的理论无关的概念。我们在我们对时空区域的状态空间的定义中使用了横纹理论方法与代数量子场理论（AQFT）建立了密切的联系。我们介绍了对称性和细胞自动机的概念，我们将其显示为以前文献中的量子蜂窝自动机（QCA）的现有定义。鉴于我们的结构的极端灵活性，我们建议将我们的框架用作AQFT，QCA和更普遍的量子场理论中新发展的起点。
We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory.
