This book is especially addressed to young researchers in theoretical physics with a basic background in Field Theory and Condensed Matter Physics. The topics were chosen so as to offer the largest possible overlap between the two expertises, selecting a few key problems in Condensed Matter Theory which have been recently revisited within a field-theoretic approach. The presentation of the material is aimed not only at providing the reader with an overview of this exciting frontier area of modern theoretical physics, but also at elucidating most of the tools needed for a technical comprehen-...

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...

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.