Algebraic quantum field theory

In J. Butterfield & J. Earman (eds.), Handbook of the philosophy of physics. Kluwer Academic Publishers (2006)
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 The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,520
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Taking Particle Physics Seriously: A Critique of the Algebraic Approach to Quantum Field Theory.David Wallace - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (2):116-125.
Bell Inequality and Common Causal Explanation in Algebraic Quantum Field Theory.Gábor Hofer-Szabó & Péter Vecsernyés - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):404-416.
Unitary Inequivalence as a Problem for Structural Realism.Steven French - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (2):121-136.
The Conventionality of Parastatistics.David John Baker, Hans Halvorson & Noel Swanson - 2014 - British Journal for the Philosophy of Science (4):axu018.

View all 12 citations / Add more citations

Similar books and articles
Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - British Journal for the Philosophy of Science 52 (3):417-470.
Philosophical Foundations of Quantum Field Theory.N. Huggett - 2000 - British Journal for the Philosophy of Science 51 (4):617-637.
Interpreting Quantum Field Theory.Laura Ruetsche - 2002 - Philosophy of Science 69 (2):348-378.
Entanglement and Open Systems in Algebraic Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (1):1-31.
Added to PP index
2009-01-28

Total downloads
139 ( #34,959 of 2,180,859 )

Recent downloads (6 months)
3 ( #104,320 of 2,180,859 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums