Coarse-Graining as a Route to Microscopic Physics: The Renormalization Group in Quantum Field Theory

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Philosophy of Science

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Leif, Hancox-Li
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The renormalization group (RG) has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory (QFT), 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.