Renormalization Methods

Originally conceived some thirty years ago in the context ofquantum electrodynamics, renormalization methods have progressivelydeveloped into an indispensable analytical tool used in widelyvarying domains of physics and applied mathematics, such as
* phase transitions and critical phenomena
* dynamical systems and chaos
* developed turbulence
* fractal structures and complex systems
* percolation
* polymer physics
* diffusion in disordered media
* measure theory and stochastic processes.
By explaining the fundamental principles of renormalization theorysuch as scale invariance and universality which lie behind all thetechnical variations, this book aims to guide the reader to a moreunified understanding of today s physics. The book is based on avery accessible main text, supplemented by several more specializedsections; it is intended for graduate students and for researcherswho are seeking an introduction to a new area of electrodynamics ora general overview of the physical phenomena to whichrenormalization methods are applied. Principles and Physical Framework.

A Comparative Study of Two Typical Examples.

Mathematical Aspects.

Statistical Mechanics.

Dynamical Systems and Chaos.

Stochastic Diffusion.

Fractal Structures.

Appendices.

Bibliography.

Index.

Annick Lesne is a Researcher at the Institut des Hautes Etudes Scientifiques. Her research lies in renormalization methods for dynamical systems, non equilibrium statistical physics, and applications of dynamical systems theory and statistical mechanics to biological systems. Originally conceived some thirty years ago in the context of quantum electrodynamics, renormalization methods have progressively developed into an indispensable analytical tool used in widely varying domains of physics and applied mathematics, such as

• phase transitions and critical phenomena
• dynamical systems and chaos
• developed turbulence
• fractal structures and complex systems
• percolation
• polymer physics
• diffusion in disordered media
• measure theory and stochastic processes.

By explaining the fundamental principles of renormalization theory ? such as scale invariance and universality ? which lie behind all the technical variations, this book aims to guide the reader to a more unified understanding of today?s physics. The book is based on a very accessible main text, supplemented by several more specialized sections; it is intended for graduate students and for researchers who are seeking an introduction to a new area of electrodynamics or a general overview of the physical phenomena to which renormalization methods are applied.