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Mathematical developments in the rise of Yang–Mills gauge theories

  • Adam KoberinskiEmail author
S.I.: Reasoning in Physics


In this paper I detail three major mathematical developments that led to the emergence of Yang–Mills theories as the foundation for the standard model of particle physics. In less than 10 years, work on renormalizability, the renormalization group, and lattice quantum field theory highlighted the utility of Yang–Mills type models of quantum field theory by connecting poorly understood candidate dynamical models to emerging experimental results. I use this historical case study to provide lessons for theory construction in physics, and touch on issues related to renormalization group realism from a more historical perspective. In particular, I highlight the fact that much of the hard work in theory construction comes when trying to understand the consequences and representational capacities of a theoretical framework.


Theory construction High-energy physics Renormalizability Yang–Mills theory 



I would like to thank Doreen Fraser, Wayne Myrvold, and Marie Gueguen for helpful comments on earlier drafts of this paper. I am also grateful to two anonymous referees, whose suggestions helped to strengthen this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Philosophy and Rotman Institute of PhilosophyUniversity of Western OntarioLondonCanada

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