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.

Table of Contents:
1 Introduction: Renormalization. 1930-1950.- 1.1. Apologia.- 1.2. Quantum Electrodynamics: 1926-1930.- 1.3. The Decade of Struggle: 1930-1940.- 1.4. The Triumph of Renormalization: The 1940s.- 2 Renormalization in Historical Perspective-The First Stage.- 2.1. Renormalization: The Disappearance and Reappearance of an Idea.- 2.2. J. J. Thompson: The Aether as Fluid and the Electromagnetic Mass.- 2.3. Lorentz: His Aether, Electron, and Program.- 2.4. Kramers: The Unexpected End of the First Phase.- 2.5. Comments and Conclusions.- 3 Tutorial on Infinities in QED.- 3.1. Introduction.- 3.2. Subtracting Infinity.- 3.3. The Perturbation Expansion.- 3.4. Feynman Graphs.- 3.5. Self-Energy Graphs and Vertex Graphs.- 3.6. Primitive Renormalization.- 3.7. The Renormalization Program.- 3.8. Discussion.- 4 New Philosophy of Renormalization: From the Renormalization Group Equations to Effective Field Theories.- 4.1. Conceptual Background.- 4.1.1. The Locality Assumption.- 4.1.2. The Operator Field Assumption.- 4.1.3. The Plenum Assumption of the Vacuum.- 4.1.4. Renormalization and the Consistency of QFT.- 4.2. Foundational Transformations.- 4.2.1. Cutoff.- 4.2.2. Symmetry and Symmetry Breaking.- 4.2.3. Scale Invariance and Renormalization Group Approach.- 4.2.4. Decoupling Theorem and Effective Field Theories.- 4.3. New Philosophy.- 5 Changing Conceptualization of Renormalization Theory.- 5.1. Introduction.- 5.2. The History of Quantum Mechanics and QFT.- 5.3. The Post-World War II Developments.- 5.4. The Changing Conceptualization of Renormalization. Effective Field Theories.- 5.5. The Ebb and Flow of Reductionism.- Appendix Historical Remarks on the Renormalization Group.- A.1. History of RG in Quantum Field Theory.- A.1.1. Renormalization and Renormalization Invariance.- A.1.2. The Birth of the Renormalization Group.- A.1.3. Creation of the RG Method in the Mid-1950s.- A.1.4. Other Early Applications of RG.- A.1.5. Further Development of RG in QFT.- A.2. RG in Critical Phenomena and Other Fields.- A.2.1. Spin Lattices.- A.2.2. Turbulence.- A.2.3. Paths of RG Expansion.- A.2.4. Two Faces of RG in QFT.- A.2.5. Functional Self-Similarity or Synthesis.- A.3. Summary.- Name Index.