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Quantum Fields as Category Algebras
Symmetry ( IF 2.940 ) Pub Date : 2021-09-17 , DOI: 10.3390/sym13091727
Hayato Saigo

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 be discussed.

中文翻译:

量子场作为范畴代数

在本文中,我们根据范畴代数和范畴状态提出了一种量子场的新方法。我们将量子场及其状态定义为类别代数和具有部分对合结构的因果类别上的状态。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论整合为范畴论结构,将量子性整合为非对易概率结构。还讨论了与量子场传统方法的概念关系,包括代数量子场论 (AQFT) 和拓扑量子场论 (TQFT)。
更新日期:2021-09-17
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