Locality and separability in algebraic quantum field theory

该项目提出了这个博士论文研究改进补助金是乔瓦尼瓦伦特的论文的重要组成部分，题为“局部性和不可分性在代数量子场论。“申请的资金（总计3000美元）旨在支持对普林斯顿大学哲学系进行为期两个月的访问，该学生将在汉斯·哈尔沃森教授的指导下工作，他也是乔瓦尼论文的共同主任，还有杰弗里·布布教授（马里兰州大学）。具体来说，在普林斯顿大学进行的研究的目标是构建一个代数公式的贾勒特分解贝尔不等式，隔离两个条件，称为参数独立性和结果独立性。这样的条件将被推广到量子场论，并将讨论它们与局域性和可分性概念的密切关系。此外，Halvorson和克利夫顿在2001年发表的一篇论文证明了在代数量子场论中，人们不能进行任何破坏两个空间分离系统之间纠缠关联的局域操作，这篇论文将进一步发展并与本论文的其他结果联系起来。该项目的目的是证明量子场论的内在不可分离性。 拟议活动的智力价值在于试图澄清空间分离系统之间的局部性和相关性的概念，这些概念在狭义相对论和量子力学中已经进行了大量讨论，但在代数量子场论的背景下尚未进行足够详细的探索。特别是，关于这一主题的文献缺乏任何重新制定的代数条件贾勒特的分解贝尔的不平等。此外，（非）可分性的概念在量子场论中还没有得到严格的形式化。鉴于高度技术性的主题，工作的兴趣不仅是哲学的物理学，而且数学物理。事实上，我们打算将研究成果提交给这两个领域的期刊。 至于拟议活动的更广泛影响，计划是通过在各种会议上就物理学基础和科学哲学进行演讲和介绍，传播Valente在Halvorson教授的监督下完成的研究成果。正是在这种精神下，人们应该理解整个论文的主要目标之一。这是对代数量子场论结构的简化讨论，这样，即使那些没有特别复杂的技术背景的人，也可以理解它的数学细节以及相关的哲学问题。

The project proposed for this Doctoral Dissertation Research Improvement Grant is an important part of Giovanni Valente's dissetation, titled "Locality and Non-Separability in Algebraic Quantum Field Theory." The requested amount of funding ($3000 in total) is intended to support a two-month visit to the Department of Philosophy at Princeton University, where the student will work under Prof. Hans Halvorson, who is also the co-director of Giovanni's dissertation, together with Prof. Jeffrey Bub (University of Maryland). Specifically, the goal of the research to be conducted in Princeton is to construct an algebraic formulation of Jarrett's decomposition of Bell's inequalities, isolating two conditions, called parameter independence and outcome independence. Such conditions will be then generalized to Quantum Field Theory and their close relation to the concepts of locality and separability will be discussed. Moreover, a paper published by Halvorson together with Clifton in 2001, which proves that in Algebraic Quantum Field Theory one cannot perform any local operation that destroys entanglement correlations between two spatially separated systems, will be further developed and connected to the other results of the dissertation. The aim of the project is to demonstrate the intrinsic non-separability of quantum field theory. The intellectual merit of the proposed activity consists in the attempt of clarifying the notions of locality and correlations between spatially separated systems, which have been largely discussed in Special Relativity and Quantum Mechanics, but have not been explored enough in detail in the context of Algebraic Quantum Field Theory. In particular, the literature on the topic lacks any re-formulation in algebraic terms of Jarrett's decomposition of the Bell's inequalities. Furthermore, the concept of (non-)separability has not received a rigorous formalization in the context of quantum field theory. Given the highly technical nature of the subject, the work is of interest not only for philosophy of physics, but also for mathematical physics. In fact, we intend to submit the resulting research papers to journals in both fields. As to the broader impacts of the proposed activity, the plan is to disseminate the results of the research accomplished by Valente under the supervision of Prof. Halvorson through talks and presentations at various meetings and conferences on foundations of physics as well as on philosophy of science. It is in this spirit that one should understand one of the major objectives of the entire dissertation. That is offering a simplified discussion of the structure of Algebraic Quantum Field Theory, so that its mathematical details, as well as the relevant philosophical issues, could be made accessible even to those who do not have a particularly sophisticated technical background.