The Real Problem with Perturbative Quantum Field Theory

The perturbative approach to quantum field theory (QFT) has long been viewed with suspicion by philosophers of science. This article offers a diagnosis of its conceptual problems. Drawing on Norton’s ([2012]) discussion of the notion of approximation I argue that perturbative QFT ought to be understood as producing approximations without specifying an underlying QFT model. This analysis leads to a reassessment of common worries about perturbative QFT. What ends up being the key issue with the approach on this picture is not mathematical rigour, or the threat of inconsistency, but the need for a physical explanation of its empirical success. 1. Three Worries about Perturbative Quantum Field Theory2. The Perturbative Formalism 2.1. Expanding the S-matrix2.2. Perturbative renormalization3. Approximations and Models4. Perturbative Quantum Field Theory Produces Approximations5. The Real Problem Three Worries about Perturbative Quantum Field Theory The Perturbative Formalism 2.1. Expanding the S-matrix2.2. Perturbative renormalization Expanding the S-matrix Perturbative renormalization Approximations and Models Perturbative Quantum Field Theory Produces Approximations The Real Problem