Renormalization: From Lorentz to Landau (and Beyond)

Abstract

The essays in this volume treat various aspects of renormalization theory in classical and quantum physics. R.S. Mills gives a simple overview of how renormalization works in quantum electrodynamics, showing how to replace the formal charge and mass parameters of the Lagrangian by the corresponding measured values, thus producing a consistent and finite theory. M. Dresden describes how the concept of renormalization developed out of problems in hydrodynamics in the 19th century, how the inchoate ideas were applied to the classical and early quantum theories of the electron and how they were formulated in a way useful for quantum electrodynamics in the late 1940s. S.S. Schweber discusses the way in which renormalization has blurred the distinction between notions of a fundamental theory and a phenomenological one. T.Y. Cao examines the notions of the renormalization group, symmetry breaking and the decoupling of high-energy processes from low-energy phenomena. L. Brown fills in the history since the 1940s, showing how the ideas formulated by Kramers in 1947 were able to be applied to produce a consistent, divergence-free theory of quantum electrodynamics which in turn became a model for effective field theories. An appendix by D.V. Shirkov describes parallel developments in the Soviet Union.