Renormalization is a mathematical operation that needs to be carried out to make empirical sense of quantum field theories (QFTs). How should renormalized QFTs be physically interpreted? A prominent non-perturbative strategy for renormalizing QFTs is to draw on formal analogies with classical statistical mechanical models for critical phenomena. This strategy is implemented in both the Wilsonian renormalization group approach and the Euclidean approach to constructing models of the Wightman axioms. Each approach features a scaling transformation, but the scaling transformations are given different interpretations. I will analyze the two interpretations and argue that the approaches offer compatible and complementary perspectives on renormalization.
Philosophy of Physics Seminar Convenors: Dr Adam Caulton and Dr Christopher Timpson