论文标题
组成量子场理论：公理表现
Compositional Quantum Field Theory: An axiomatic presentation
论文作者
论文摘要
我们基于局部和组成性的原理，将组成量子场理论（CQFT）作为量子场理论的公理模型。我们的模型是对一般边界量子场理论的公理的改进，并根据对应的某些通勤图与状态空间和线性图的相应通勤图之间的粘合识别图之间的对应关系进行了措辞，从而使其可根据涉及对称的单型单型功能和操作范围和术语来使其正式化。胶合胶的基本新型框架可导致CQFT的模棱两可。我们在维度2中研究CQFT，以及它们在开放和封闭字符串上定义的代数结构。我们还将二维纯量子阳米尔斯理论的组成结构视为一种特殊情况。
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field Theory, and is phrased in terms of correspondences between certain commuting diagrams of gluing identifications between manifolds and corresponding commuting diagrams of state-spaces and linear maps, thus making it amenable to formalization in terms of involutive symmetric monoidal functors and operad algebras. The underlying novel framework for gluing leads to equivariance of CQFT. We study CQFTs in dimension 2 and the algebraic structure they define on open and closed strings. We also consider, as a particular case, the compositional structure of 2-dimensional pure quantum Yang-Mills theory.
