In J. Butterfield & J. Earman (eds.), Handbook of the philosophy of physics. Kluwer Academic Publishers (2006)

Authors
Hans Halvorson
Princeton University
Abstract
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.
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Scientific Realism Made Effective.Porter Williams - 2019 - British Journal for the Philosophy of Science 70 (1):209-237.
Taking Particle Physics Seriously: A Critique of the Algebraic Approach to Quantum Field Theory.David Wallace - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (2):116-125.
Against Field Interpretations of Quantum Field Theory.David John Baker - 2009 - British Journal for the Philosophy of Science 60 (3):585-609.
Between Classical and Quantum.Nicolaas P. Landsman - 2007 - Handbook of the Philosophy of Science 2:417--553.
The Real Problem with Perturbative Quantum Field Theory.James D. Fraser - 2020 - British Journal for the Philosophy of Science 71 (2):391-413.

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