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Haag's theorem, apparent inconsistency, and the empirical adequacy of quantum field theory

Miller, Michael (2015) Haag's theorem, apparent inconsistency, and the empirical adequacy of quantum field theory. [Preprint]

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Abstract

Haag's theorem has been interpreted as establishing that quantum field theory cannot consistently represent interacting fields. Earman and Fraser have clarified how it is possible to give mathematically consistent calculations in scattering theory despite the theorem. However, their analysis does not fully address the worry raised by the result. In particular, I argue that their approach fails to be a complete explanation of why Haag's theorem does not undermine claims about the empirical adequacy of particular quantum field theories. I then show that such empirical adequacy claims are protected from Haag's result by the techniques that are required to obtain theoretical predictions for realistic experimental observables. I conclude by showing how Haag's theorem is illustrative of a general tension between the foundational significance of results that can be obtained in perturbation theory and non-perturbative characterizations of the content of quantum field theory.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Miller, Michaelmichael.earl.miller@gmail.com
Keywords: Quantum field theory, Haag's theorem, inconsistency, empirical adequacy
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
General Issues > Structure of Theories
General Issues > Theory/Observation
Depositing User: Mr. Michael E. Miller
Date Deposited: 13 Sep 2015 00:58
Last Modified: 15 Aug 2016 20:31
Item ID: 11673
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
General Issues > Structure of Theories
General Issues > Theory/Observation
Date: 12 September 2015
URI: http://philsci-archive.pitt.edu/id/eprint/11673

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