Renormalization Methods

• Easy introduction to the use of renormalization methods.
• Bridges the gap between elementary texts and advanced texts on statistical field theory and critical phenomena.
• Uses only basic physics and mathematics; accessible to a wide readership of scientists, engineers and mathematicians.
• Addresses deep fundamental concepts whilst remaining a careful exposition for students of all levels of ability.
• Supplemented with exercises and appendices to give a complete understanding of the main text.

Readership: Aimed at final-year undergraduate, postgraduate and research physicists. Also of interest to applied mathematicians, fluid dynamicists, mechanical and chemical engineers, and physical chemists.

William David McComb, School of Physics, University of Edinburgh, UK

Review(s) from previous edition

"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. - 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

What is renormalization?
1: The bedrock problem: why we need renormalization methods
2: Easy applications of renormalization group (RG) to simple models
3: Mean-field theories for simple models
Renormalized perturbation theories (RPT)
4: Perturbation theory using a control parameter
5: Classical nonlinear systems driven by random noise
6: Application of RPT to turbulence and related problems
Renormalization group
7: Setting the scene: critical phenomena
8: Real-space RG
9: Momentum-space RG
10: Field-theoretic RG
11: Dynamical RG applied to classical nonlinear systems
Appendices
A: Statistical ensembles
B: From statistical mechanics to thermodynamics
C: Exact solutions in one and two dimensions
D: Quantum treatment of the Hamiltonian N-body assembly
E: Generalization of the Bogoliubov variational method to a spatially-varying magnetic field

Download the Solutions PDF