TOPOLOGY IN MODERN QUANTUM PHYSICS AND FIELD THEORY

Credit Hours: 3 · Graduate

Topology plays an increasingly important role in modern quantum physics, and its applications to a variety of topics range from the theory of liquid crystals to topological defects in quantum field theory. This course will introduce some key notions from topology, such as homotopy and homology, and differential geometry and discuss their applications in quantum physics, from the theory of vortices in superconductors, to monopoles in non-Abelian gauge theories, to instantons in Yang—Mills theory. The course also covers the concepts of topological insulators and superconductors that have become an important part of the vocabulary of modern condensed matter physics. The course may be useful for students pursuing research in condensed matter and AMO physics, as well as high-energy physicists interested in topological defects in quantum field theory.