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- 1.: Introduction and Ancient History
- 2.: Kauffman Bracket Invariant and Relation to Physics
- I Anyons and Topological Quantum Field Theories
- 3.: Particle Quantum Statistics
- 4.: Aharonov-Bohm Effect and Charge-Flux Composites
- 5.: Chern-Simons Theory Basics
- 6.: Short Digression on Quantum Gravity
- 7.: Defining Topological Quantum Field Theory
- II Anyon Basics
- 8.: Fusion and Structure of Hilbert Space
- 9.: Change of Basis and F-Matrices
- 10.: Exchanging Identical Particles
- 11.: Computing with Anyons
- III Anyon Diagrammatics
- 12.: Planar Diagrams
- 13.: Braiding Diagrams
- 14.: Seeking Isotopy
- 15.: Twists
- 16.: Nice Theories with Planar or Three-Dimensional Isotopy
- 17.: Further Structure
- IV Some Examples: Planar Diagrams and Anyon Theories
- 18.: Some Simple Examples
- 19.: Anyons From Discrete Groups Elements
- 20.: Bosons and Fermions from Group Representati
- 21.: Quantum Groups (In Brief)
- 22.: Temperly-Lieb Algebra and Jones-Kauffman Anyons
- V Applications of TQFT Diagrammatics
- 23.: State Sum TQFTs
- 24.: Formal Construction of "Chern-Simons" TQFT: Surgery and More Complicated Manifolds
- 25.: Anyon Condensation
- VI Toric Code Basics
- 26.: Introducing Quantum Error Correction
- 27.: Introducing the Toric Code
- 28.: The Toric Code as a Phase of Matter and a TQFT
- 29.: Robustness of Topologically-Ordered Matter
- 30.: Abstracting the Toric Code: Introduction to Tube Algebra
- VII More General Loop-Gas and String-Net Models
- 31.: Kitaev Quantum Double Model
- 32.: Doubled-Semion Model
- 33.: Levin-Wen String-Net
- VIII Entanglement and Symmetries
- 34.: Topological Entanglement
- 35.: SPT Phases of Matter
- 36.: Anyon Permuting Symmetry
- IX Further Thoughts
- 37.: 37 Experiments (In Brief)
- 38.: Final Comments
- 39.: Appendix: Kac and Other Resources for TQFTs
- 40.: Appendix: Some Mathematical Basics
- Index
- Free
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Mechanik & Akustik |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 640 |
| ISBN-13: | 9780198886723 |
| ISBN-10: | 0198886721 |
| Einband: | Gebunden |
| Autor: | Simon, Steven H. |
| Hersteller: | Oxford University Press |
| Maße: | 250 x 189 x 41 mm |
| Von/Mit: | Steven H. Simon |
| Erscheinungsdatum: | 29.09.2023 |
| Gewicht: | 1,528 kg |
- 1.: Introduction and Ancient History
- 2.: Kauffman Bracket Invariant and Relation to Physics
- I Anyons and Topological Quantum Field Theories
- 3.: Particle Quantum Statistics
- 4.: Aharonov-Bohm Effect and Charge-Flux Composites
- 5.: Chern-Simons Theory Basics
- 6.: Short Digression on Quantum Gravity
- 7.: Defining Topological Quantum Field Theory
- II Anyon Basics
- 8.: Fusion and Structure of Hilbert Space
- 9.: Change of Basis and F-Matrices
- 10.: Exchanging Identical Particles
- 11.: Computing with Anyons
- III Anyon Diagrammatics
- 12.: Planar Diagrams
- 13.: Braiding Diagrams
- 14.: Seeking Isotopy
- 15.: Twists
- 16.: Nice Theories with Planar or Three-Dimensional Isotopy
- 17.: Further Structure
- IV Some Examples: Planar Diagrams and Anyon Theories
- 18.: Some Simple Examples
- 19.: Anyons From Discrete Groups Elements
- 20.: Bosons and Fermions from Group Representati
- 21.: Quantum Groups (In Brief)
- 22.: Temperly-Lieb Algebra and Jones-Kauffman Anyons
- V Applications of TQFT Diagrammatics
- 23.: State Sum TQFTs
- 24.: Formal Construction of "Chern-Simons" TQFT: Surgery and More Complicated Manifolds
- 25.: Anyon Condensation
- VI Toric Code Basics
- 26.: Introducing Quantum Error Correction
- 27.: Introducing the Toric Code
- 28.: The Toric Code as a Phase of Matter and a TQFT
- 29.: Robustness of Topologically-Ordered Matter
- 30.: Abstracting the Toric Code: Introduction to Tube Algebra
- VII More General Loop-Gas and String-Net Models
- 31.: Kitaev Quantum Double Model
- 32.: Doubled-Semion Model
- 33.: Levin-Wen String-Net
- VIII Entanglement and Symmetries
- 34.: Topological Entanglement
- 35.: SPT Phases of Matter
- 36.: Anyon Permuting Symmetry
- IX Further Thoughts
- 37.: 37 Experiments (In Brief)
- 38.: Final Comments
- 39.: Appendix: Kac and Other Resources for TQFTs
- 40.: Appendix: Some Mathematical Basics
- Index
- Free
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Mechanik & Akustik |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 640 |
| ISBN-13: | 9780198886723 |
| ISBN-10: | 0198886721 |
| Einband: | Gebunden |
| Autor: | Simon, Steven H. |
| Hersteller: | Oxford University Press |
| Maße: | 250 x 189 x 41 mm |
| Von/Mit: | Steven H. Simon |
| Erscheinungsdatum: | 29.09.2023 |
| Gewicht: | 1,528 kg |
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