作为范畴代数的量子场
Quantum Fields as Category Algebras
摘要：
本文从范畴代数和范畴上的态出发，提出了一种研究量子场的新方法。我们将量子场和量子态定义为范畴代数和具有部分对合结构的因果范畴上的量子态。通过利用范畴代数和范畴上的状态而不是简单地考虑范畴，我们可以直接将相对性作为范畴论结构，将量子性作为非交换概率结构。与传统的量子场的方法，包括代数量子场论（AQFT）和拓扑量子场论（TQFT）的概念关系，也进行了讨论。
英文摘要：
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also discussed.
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