New Philosophy of Renormalization: From the Renormalization Group Equations to Effective Field Theories

Abstract

The conceptual foundations of renormalization theory has undergone radical transformations during the last four decades. These changes are the result both of attempts to solve conceptual anomalies within the theory itself, and of fruitful interactions between quantum field theory (QFT) and statistical physics. Implicit assumptions concerning such concepts as regularization, cutoff, dimensionality, symmetry, and renormalizability have been clarified, and the original understanding of these concepts is being transformed. New concepts involve symmetry breaking, either spontaneous or anomalous, renormalization group transformations, decoupling of high-energy processes from low-energy phenomena, sensible nonrenormalizable theories, and effective field theories. These have been developed, drawing heavily on dramatic progress in statistical physics. The purpose of this essay is to examine these foundational transformations (Sec. 4.2), and to show that these advances have led to a new understanding of renormalization, a clarification of the theoretical structure of QFT and its ontological basis, and most importantly, a radical shift of outlook in fundamental physics (Sec. 4.3). For this purpose, however, a clarification of the conceptual background is indispensable (Sec. 4.1).