Locality and separability in algebraic quantum field theory

University Of Maryland, College Park, College Park MD

Investigators

Abstract

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.