This book explores the fractionalization of particles in physics, how interactions between individual particles and with their background can modify their fundamental quantum states. Covering a large breadth of topics with an example-driven approach, this comprehensive text explains why phases of matter must be described in terms of both symmetries and their topology. The majority of important results are derived in full with explanations provided, while exercises at the end of each section allow readers to extend and develop their understanding of key topics. The first part presents polyacetylene as the paradigmatic material in which electric charge can be fractionalized, while the second part introduces the notion of invertible topological phases of matter. The final part is devoted to the 'ten-fold way', a classification of topological insulators or superconductors. The text requires a solid understanding of quantum mechanics and is a valuable resource for graduate students and researchers in physics.

About the Authors

Christopher Mudry is Head of the Condensed Matter Theory Group at the Paul-Scherrer Institute. He earned his Ph.D. in theoretical physics from the University of Illinois at Urbana-Champaign and his research is focused on condensed condensed matter physics.

Claudio Chamon is Professor of Physics at Boston University. He earned his Ph.D. in Physics from MIT and his research interests are in condensed matter physics and in quantum and classical computation.

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