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In solid-state physics especially topological techniques have turned out to be extremely useful for modelling and explaining physical properties of matter. This book illustrates various applications of algebraic topology in classical field theory (non-linear sigma-models) and in quantizationsin multiply connected spaces (anyons). It treats Chern-Simon Lagrangians, Berry's phase, the polarization of light and the fractional quantum Hall effect.

Discussing the foundations of both classical and quantum statistical mechanics, this book aims to bridge a gap that exists between standard textbooks on the subject and more advanced books. It is devised for a one-semester course on statistical mechanics at the graduate level. Its prerequisite is therefore a more elementary course on the same subject. Emphasis is laid on the geometrical aspects of classical thermodynamics, on the foundational problems, and on selected applications, mainly to spin systems, the meaning of quantum statistics, phase transitions, critical phenomena and the...

This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks.