Renormalization Methods
A Guide For Beginners
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Product details:
- Publisher OUP Oxford
- Date of Publication 11 December 2003
- ISBN 9780198506942
- Binding Hardback
- No. of pages348 pages
- Size 248x173x23 mm
- Weight 764 g
- Language English
- Illustrations numerous figures 0
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Short description:
There is currently widespread interest in applications of renormalization methods to various topics ranging from fluid turbulence to fluctuations in the stock market. This book is unique in demystifying this material for non-specialists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.
MoreLong description:
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 interpretation (and motivation), including mean-field theories and high-temperature and low-density expansions. It then proceeds by easy 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 queueing 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 physicists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.
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.
Table of Contents:
What is renormalization?
The bedrock problem: why we need renormalization methods
Easy applications of renormalization group (RG) to simple models
Mean-field theories for simple models
Renormalized perturbation theories (RPT)
Perturbation theory using a control parameter
Classical nonlinear systems driven by random noise
Application of RPT to turbulence and related problems
Renormalization group
Setting the scene: critical phenomena
Real-space RG
Momentum-space RG
Field-theoretic RG
Dynamical RG applied to classical nonlinear systems
Appendices
Statistical ensembles
From statistical mechanics to thermodynamics
Exact solutions in one and two dimensions
Quantum treatment of the Hamiltonian N-body assembly
Generalization of the Bogoliubov variational method to a spatially-varying magnetic field
