论文标题
量子场逻辑
Quantum field logic
论文作者
论文摘要
代数量子场理论或简称AQFT是对相对论量子力学结构的严格分析。它是根据洛伦兹歧管区域索引的运算符代数的网表示的。在某些情况下，上述网由von Neumann代数的家族代表，具体，III型因子。局部量子场逻辑作为逻辑系统产生，该系统捕获了网络代数中编码的命题结构。在此框架中，这项工作有助于解决一个自30年代以来的开放问题家族的解决方案，这些逻辑系统的表征可以通过默里 - 冯·诺伊曼（Murray-Von Neumann）的因素分类而识别为投影仪的晶格。更确切地说，基于AQFT中正式描述的物理要求，可以在因子中表征III型条件的方程理论。该方程式系统激发了对具有潜在矫形晶格结构的各种代数的研究。还介绍了一种在上述变体中代数的希尔伯特风格的微积分，并建立了相应的完整性定理。
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several cases the mentioned net is represented by a family of von Neumann algebras, concretely, type III factors. Local quantum field logic arises as a logical system that captures the propositional structure encoded in the algebras of the net. In this framework, this work contributes to the solution of a family of open problems, emerged since the 30s, about the characterization of those logical systems which can be identified with the lattice of projectors arising from the Murray-von Neumann classification of factors. More precisely, based on physical requirements formally described in AQFT, an equational theory able to characterizethe type III condition in a factor is provided. This equational system motivates the study of a variety of algebras having an underlying orthomodular lattice structure. A Hilbert style calculus, algebraizable in the mentioned variety, is also introduced and a corresponding completeness theorem is established.
