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Solutions in Constructive Field Theory

Published online by Cambridge University Press:  01 January 2022

Leif Hancox-Li
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Abstract

Constructive field theory aims to rigorously construct concrete, nontrivial solutions to Lagrangians used in particle physics. I examine the relationship of solutions in constructive field theory to both axiomatic and Lagrangian quantum field theory (QFT). I argue that Lagrangian QFT provides conditions for what counts as a successful constructive solution and other information that guides constructive field theorists to solutions. Solutions matter because they describe the behavior of QFT systems and thus what QFT says the world is like. Constructive field theory clarifies existing disputes about which parts of QFT are philosophically relevant and how rigor relates to these disputes.

Type
Research Article
Information
Philosophy of Science , Volume 84 , Issue 2 , April 2017 , pp. 335 - 358
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I thank Bob Batterman and Michael Miller for comments and encouragement. Several anonymous referees also contributed valuable comments.

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