Locality and separability in algebraic quantum field theory

为这篇博士论文提出的研究改进补助金是乔瓦尼·瓦伦特的著作《代数量子场论中的局部性和不可分离性》的重要组成部分。申请的资助金额(总计3000美元)旨在支持对普林斯顿大学哲学系为期两个月的访问，学生将在那里的汉斯·哈尔沃森教授和杰弗里·布布教授(马里兰大学)一起工作，哈沃森教授也是乔瓦尼论文的联合主任。具体地说，这项将在普林斯顿进行的研究的目标是构建Jarrett分解贝尔不等式的代数公式，分离出两个条件，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，并讨论它们与局域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，在代数量子场论中，一个人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，该论文将进一步发展并与论文的其他结果相联系。该项目的目的是证明量子场论的内在不可分性。拟议活动的学术价值在于试图澄清空间上分离的系统之间的局域性和相关性的概念，这些概念在狭义相对论和量子力学中已经有很大讨论，但在代数量子场论的背景下还没有得到足够详细的探索。特别是，关于这一主题的文献缺乏任何关于Jarrett对贝尔不等式的分解的代数形式的重新表述。此外，在量子场论的背景下，(不可)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哲学感兴趣，而且对数学物理也很感兴趣。事实上，我们打算向这两个领域的期刊提交由此产生的研究论文。至于拟议活动的更广泛影响，计划通过在各种关于物理学基础和科学哲学的会议和会议上的演讲和演讲，传播瓦伦特在哈尔沃森教授的指导下完成的研究成果。正是本着这种精神，我们应该理解整篇论文的主要目的之一。这是对代数量子场论结构的简化讨论，以便即使那些没有特别复杂的技术背景的人也可以接触到它的数学细节和相关的哲学问题。

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.