Renormalization Methods - McComb, William David

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Résumé :
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....

Biographie:
Professor William David McComb Professor of Statistical Physics University of Edinburgh Senior Scientific Officer, Theoretical Physics Division, Atomic Energy Research Establishment, Harwell (1969-71). Lecturer, Reader and Professor, Edinburgh University (1971-present time). Guest Professor, Technical University of Delft, Netherlands (August-November 1997). Visiting Fellow, Wolfson College, Cambridge (January-July 1999)....

Sommaire:

• 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