Locality and separability in algebraic quantum field theory

本次博士论文研究改进基金项目是Giovanni Valente博士论文《代数量子场论中的局部性和不可分性》的重要组成部分。所申请的资金总额（3000美元）旨在支持该学生在普林斯顿大学哲学系进行为期两个月的访问，该学生将在Hans Halvorson教授（也是Giovanni论文的联合主任）和Jeffrey Bub教授（马里兰大学）的指导下工作。具体来说，在普林斯顿进行的研究的目标是构建Jarrett分解Bell不等式的代数公式，分离两个条件，称为参数独立性和结果独立性。然后将这些条件推广到量子场论，并讨论它们与局部性和可分性概念的密切关系。此外，Halvorson和Clifton在2001年发表的一篇论文证明了在代数量子场论中不能进行任何破坏两个空间分离系统之间纠缠关联的局部运算，这篇论文将进一步发展并与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性。提出的活动的智力价值在于试图澄清局部性和空间分离系统之间的相关性的概念，这在狭义相对论和量子力学中已经得到了很大的讨论，但在代数量子场论的背景下还没有得到足够的详细探讨。特别是，关于该主题的文献缺乏任何在代数方面的Jarrett的贝尔不等式分解的重新表述。此外，在量子场论的背景下，（非）可分性的概念还没有得到严格的形式化。鉴于这门学科的高度技术性，这项工作不仅对物理学哲学，而且对数学物理学都有意义。事实上，我们打算将最终的研究论文提交给两个领域的期刊。至于拟议活动的更广泛影响，计划是通过在各种物理基础和科学哲学会议上的演讲和报告，传播Valente在Halvorson教授指导下所完成的研究成果。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。这提供了一个关于代数量子场论结构的简化讨论，这样它的数学细节，以及相关的哲学问题，即使对那些没有特别复杂的技术背景的人来说，也是可以理解的。

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.