📗 Libro en inglés RENORMALIZATION METHODS: A GUIDE FOR BEGINNERS

William David McComb, W. D. McComb

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 meanfield 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. Normalization of Fourier integrals p. 1 Notation for Chapters 1-4 and 7-10 p. 2 Notation for Chapters 5, 6, and 11 p. 4 What is Renormalization? The bedrock problem: why we need renormalization methods p. 7 Easy applications of Renormalization Group to simple models p. 53 Mean-field theories for simple models p. 71 Renormalized Perturbation Theories Perturbation theory using a control parameter p. 87 Classical nonlinear systems driven by random noise p. 110 Application of renormalized perturbation theories to turbulence and related problems p. 129 Renormalization Group (RG) Setting the scene: critical phenomena p. 147 Real-space Renormalization Group p. 182 Momentum-space Renormalization Group p. 197 Field-theoretic Renormalization Group p. 228 Dynamical Renormalization Group applied to classical nonlinear system p. 260 Appendices Statistical ensembles p. 295 From statistical mechanics to thermodynamics p. 304 Exact solutions in one and two dimensions p. 310 Quantum treatment of the Hamiltonian N-body assembly p. 313 Generalization of the Bogoliubov variational method to a spatially varying magnetic field p. 318 References p. 320 Index p. 323 Table of Contents provided by Blackwell.