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What is renormalization? | |
The bedrock problem:why we need renormalization methods | |
Easy applications of renomalization group (RG) to simple models | |
Mean-field theories for simple models Renormalization 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 pehnomena | |
Real-space RG | |
Momentum-space RG | |
Field-theoretic RG | |
Dynamical RG applied to classic 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 | |
Table of Contents provided by Publisher. All Rights Reserved. |
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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.
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