Condensed Matter Physics and Topology - From the Viewpoint of Noncommutative Geometry
2023-03-29
Book
Author: Yosuke Kubota
Language: Japanese
Description
This book summarizes part of the theory of topological phases of matter in condensed matter physics, especially from a mathematical standpoint. In particular, we have tried to give an overview of the field as much as possible, focusing on two main topics: classification of topological phases and mathematical proofs of bulk and boundary correspondences.
Table of contents
- Introduction
- Preparations from Functional Analysis
- Index Theory of Fredholm Operators
- K-Theory of Operator Algebras
- Complex Topological Insulators
- Noncommutative Geometry of Random Operators
- Coarse Geometry and Topological Phases
- Topological Insulators and Real K-Theory
- Spectral Localizers
- Twisted equivariant K-Theory
- Topological Crystalline insulator
- Related Topics
- Appendix