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The development of renormalization group methods for particle physics: Formal analogies between classical statistical mechanics and quantum field theory

Fraser, Doreen (2018) The development of renormalization group methods for particle physics: Formal analogies between classical statistical mechanics and quantum field theory. [Preprint]

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Abstract

Analogies between classical statistical mechanics (CSM) and quantum field theory (QFT) played a pivotal role in the development of renormalization group (RG) methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's (Wilson and Kogut 1974). The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics.


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Item Type: Preprint
Creators:
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Fraser, Doreen
Keywords: analogies, quantum field theory, statistical mechanics, particle physics, renormalization group methods, Kenneth G. Wilson
Subjects: Specific Sciences > Physics > Condensed Matter
General Issues > Explanation
General Issues > History of Science Case Studies
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Doreen Fraser
Date Deposited: 26 Apr 2018 11:58
Last Modified: 26 Apr 2018 11:58
Item ID: 14591
Subjects: Specific Sciences > Physics > Condensed Matter
General Issues > Explanation
General Issues > History of Science Case Studies
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 25 April 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14591

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