Renormalization group methods and the epistemology of effective field theories

The effective field theory (EFT) perspective on particle physics has yielded insight into the Standard Model. This paper investigates the epistemic consequences of the use of different variants of renormalization group (RG) methods as part of the EFT perspective on particle physics. RG methods are a family of formal techniques. While the semi-group variant of the RG has played a prominent role in condensed matter physics, the full-group variant has become the most widely applicable formalism in particle physics. We survey different construction techniques for EFTs in particle physics and analyze the role that semi-group and full-group variants of the RG play in each. We argue that the full-group variant is best suited to answering structural questions about relationships among EFTs at different scales, as well as explanatory questions, such as why the Standard Model has been empirically successful at low energy scales and why renormalizability was a successful criterion for constructing the Standard Model. We also present an account of EFTs in particle physics that is based on the full-RG. Our conclusion about the advantages of the full-RG is restricted to the particle physics case. We argue that a domain-specific approach to interpreting EFTs and RG methods is needed. Formal variations and flexibility in physical interpretation enable RG methods to support different explanatory strategies in condensed matter and particle physics. In particular, it is consistent to maintain that coarse-graining is an essential component of explanations in condensed matter physics, but not in particle physics.