Staying on-shell: manifest properties and reformulations in particle physics

Abstract The empirical success of particle physics rests largely on an approximation method: perturbation theory. Yet even within perturbative quantum field theory, there are a variety of different formulations. This variety teaches us that reformulating approximation methods can provide a tremendous source of progress in science. Along with enabling the solution of otherwise intractable problems, reformulations clarify what we need to know to obtain solutions, which can in turn make previously hidden properties manifest. To develop these lessons, I compare and contrast three compatible formulations of perturbative QFT: (i) elementary perturbation theory, (ii) the method of Feynman diagrams, and (iii) a recent reformulation known as on-shell recursion. I propose and defend a novel account of what it means to ‘make a property manifest,’ based on the inferences that a formulation warrants.