Renormalization methods :
McComb, W. D.
Renormalization methods : a guide for beginners / W. D. McComb. - First Edition - xviii, 330 pages : illustrated ; 25 cm.
Includes index.
Includes bibliographical references (pages [320]-321).
I. What is Renormalization? -- 1. bedrock problem: why we need renormalization methods -- 2. Easy applications of Renormalization Group to simple models -- 3. Mean-field theories for simple models -- II. Renormalized Perturbation Theories -- 4. Perturbation theory using a control parameter -- 5. Classical nonlinear systems driven by random noise -- 6. Application of renormalized perturbation theories to turbulence and related problems -- III. Renormalization Group (RG) -- 7. Setting the scene: critical phenomena -- 8. Real-space Renormalization Group -- 9. Momentum-space Renormalization Group -- 10. Field-theoretic Renormalization Group -- 11. Dynamical Renormalization Group applied to classical nonlinear system -- IV. 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.
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.
9780199236527 (pbk.) 0199236526 (pbk.)
2008274464
GBA765952 bnb
013823442 Uk
Renormalization (Physics)
Quantum field theory
Mathematical physics
Renormalización (Física)
Teoría del campo cuántico
Física matemática
530.143
Renormalization methods : a guide for beginners / W. D. McComb. - First Edition - xviii, 330 pages : illustrated ; 25 cm.
Includes index.
Includes bibliographical references (pages [320]-321).
I. What is Renormalization? -- 1. bedrock problem: why we need renormalization methods -- 2. Easy applications of Renormalization Group to simple models -- 3. Mean-field theories for simple models -- II. Renormalized Perturbation Theories -- 4. Perturbation theory using a control parameter -- 5. Classical nonlinear systems driven by random noise -- 6. Application of renormalized perturbation theories to turbulence and related problems -- III. Renormalization Group (RG) -- 7. Setting the scene: critical phenomena -- 8. Real-space Renormalization Group -- 9. Momentum-space Renormalization Group -- 10. Field-theoretic Renormalization Group -- 11. Dynamical Renormalization Group applied to classical nonlinear system -- IV. 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.
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.
9780199236527 (pbk.) 0199236526 (pbk.)
2008274464
GBA765952 bnb
013823442 Uk
Renormalization (Physics)
Quantum field theory
Mathematical physics
Renormalización (Física)
Teoría del campo cuántico
Física matemática
530.143