Renormalization scrutinized

Abstract

In this paper, I propose a general framework for understanding renormalization by drawing on the distinction between effective and continuum Quantum Field Theories (QFTs), and offer a comprehensive account of perturbative renormalization on this basis. My central claim is that the effective approach to renormalization provides a more physically perspicuous, conceptually coherent and widely applicable framework to construct perturbative QFTs than the continuum approach. I also show how a careful comparison between the two approaches: (i) helps to dispel the mystery surrounding the success of the renormalization procedure; (ii) clarifies the various notions of renormalizability; and (iii) gives reasons to temper Butterfield and Bouatta's claim that some continuum QFTs are ripe for metaphysical inquiry (Butterfield and Bouatta, 2014).

Regularizing (away) vacuum energy

“…6 For a more detailed analysis of the differences between the two approaches to renormalization, see Williams (2018) and Rivat (2019). The latter argues that EFTs are best understood strictly under cutoff regularization.…”

On the scale hierarchy in radiative symmetry breaking

“…where Λ is the ultraviolet cut-off parameter of the loop integral. Within the framework of the effective models ideology [1] this parameter sets the scale at which the chosen model (1) obviously stops working, for example, due to the quantum gravity effects switching-on. The contribution of the fermion loops is obtained in the similar way, it has the same structure:…”

“…However, in the effective theory approach, this scale takes on a very specific physical meaning: it becomes the boundary of the applicability region of the low-energy effective model [1]. In this paper, we discuss the physical meaning and the procedure of determination of the scale invariance violation parameter in the Coleman-Weinberg mechanism by the example of a simple model with one scalar self-interacting field of type ϕ 4 and one fermion field with Yukawa interaction.…”

Renormalization group methods and the epistemology of effective field theories

“…The details of renormalization are outside the scope of this paper, but seeHuggett (2002),Butterfield andBouatta (2016), andRivat (2019) for some contrasting philosophical accounts.…”