Böcker av Antonio Sergio Teixeira (Universidade Federal de Minas Gerais Pires

Concepts drawn from topology and differential geometry have become essential to the understanding of several phenomena in condensed matter physics. This book provides a self-consistent introduction to the mathematical ideas and methods from these fields that will enable the student of condensed matter physics to begin applying these concepts with confidence. This expanded second edition adds eight new chapters, including one on the classification of topological states of topological insulators and superconductors and another on Weyl semimetals, as well as elaborated discussions of the Aharonov-Casher effect, topological magnon insulators, topological superconductors and K-theory.Key Features: Provides an introduction to path integral formalism Introduces all the basic concepts in differential geometry and topology Presents the quantum Hall effect using topology conceptsIncludes an introduction to topological insulatorsPresents the Weyl semimetal using topological conceptsStudies spin systems using topology

This book is dedicated to the study of theoretical tools in spin models in magnetism. It presents the basic tools to treat spin models in magnetic systems such as: spin waves, Schwinger bosons formalism, Self-consistent harmonic approximation, Kubo theory, Perturbation theory using Green's function. Some important areas of interest in magnetism today are spin liquids and magnon topological insulators, both of which are discussed in the book.