Bihui Li

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory, but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational import on grounds of lack of rigor

I describe some interpretive strategies used by physicists in the development of quantum electrodynamics in the 1930s and 1940s, using Wimsatt's account of how to reason with false models as a guide. I call these “interpretive” strategies because they were used not just to derive empirical predictions, but also to derive information about the world besides the aforementioned predictions. These strategies were regarded as mathematically unrigorous, yet they were crucial to the development of a better theory of quantum electrodynamics. I argue that these strategies are not easily assimilated into conventional axiomatic, deductivist views of what theories tell us about the world. Furthermore, it is unclear if these strategies are necessarily less reliable than strategies based solely on mathematically rigorous inferences. I suggest that these less than fully rigorous strategies are worth considering as general strategies for working with theories in physics.

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational import on grounds of lack of rigor