Synopses & Reviews
This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretations (and motivation), including mean fields theories and high-temperature and low-density expansions. It then process by each steps to the famous epsilon expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays there is widespread interest in applications of renormalization methods to various topics ranging over soft condensed matter,engineering dynamics, traffic queuing and fluctuations in the stock market. Hence macroscopic systems are also included with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoretical physics, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.
Review
"Renormalization Methods should be an excellent source of material for anyone who plans to lead advanced undergradutes and first-year graduate students beyond the standard course material toward current research topics. I shall certainly keep the book in close reach when preparing for my classes."--Physics TodayIR
"I think this book is the best introductory textbook on techniques of renormalization available. It will be a delight to read for anyone who is encountering the topic for the first time and is wishing to exploit the methods to pass an exam or in one's field."--Contemporary Physics
Review
"One can hope that this book will stimulate interest in bringing the theories of nonlinear dissipative systems up to the level of understanding of the familiar and largely solved problems of conservative statistical physics."--
The Journal of Fluid Mechanics"Requiring only the basic physics and mathematics known to most scientists and engineers, the material should be accessible to readers other then theoretical physicists."--CERN Courier
"Renormalization Methods should be an excellent source of material for anyone who plans to lead advanced undergradutes and first-year graduate students beyond the standard course material toward current research topics. I shall certainly keep the book in close reach when preparing for my classes."--Physics Today
"I think this book is the best introductory textbook on techniques of renormalization available. It will be a delight to read for anyone who is encountering the topic for the first time and is wishing to exploit the methods to pass an exam or in one's field."--Contemporary Physics
"this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theorythe book should at least find a place on most library reference shelves."--Journal of Physics A: Mathematics and General
"All in all, the author succeeds in what he sets out to do, and the somewhat unusual emphasis on fluid flow problems makes this an interesting read."--Theoretical Physics Book Reviews
About the Author
Professor William David McComb is a professor of Statistical Physics at the Univeristy of Edinburgh
Table of Contents
What is renormalization?
Chapter 1. The bedrock problem:why we need renormalization methods
Chapter 2. Easy applications of renomalization group (RG) to simple models
Chapter 3. Mean-field theories for simple models
Renormalization perturbation theories (RPT)
Chapter 4. Perturbation theory using a control parameter
Chapter 5. Classical nonlinear systems driven by random noise
Chapter 6. Application of RPT to turbulence and related problems
Renormalization group
Chapter 7. Setting the scene: critical pehnomena
Chapter 8. Real-space RG
Chapter 9. Momentum-space RG
Chapter 10. Field-theoretic RG
Chapter 11. Dynamical RG applied to classic nonlinear systems
Appendices
Chapter A. Statistical ensembles
Chapter B. From statistical mechanics to thermodynamics
Chapter C. Exact Solutions in one and two dimensions
Chapter D. Quantum Treatment of the Hamiltonian N-body assembly
Chapter E. Generalization of the Bogoliubov variational method to a spatially-varying magnetic field