| Description |
1 online resource (v, 96 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1251 |
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Memoirs of the American Mathematical Society ; no. 1251.
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| Contents |
1. Introduction -- 2. Basic Definitions and Simple Examples -- 3. Topological Structures -- 4. Topological Spinor Bundles -- 5. Further Examples -- 6. Tangent Cone Measures and the Tangential Clifford Section -- 7. The Topology of Discrete and Singular Fermion Systems -- 8. Basic Examples -- 9. Spinors on Singular Spaces |
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Chapter 1. Introduction -- Chapter 2. Basic Definitions and Simple Examples -- Chapter 3. Topological Structures -- 3.1. A Sheaf -- 3.2. A Topological Vector Bundle -- 3.3. A Bundle over a Topological Manifold -- 3.4. A Bundle over a Differentiable Manifold -- Chapter 4. Topological Spinor Bundles -- 4.1. Clifford Sections -- 4.2. Topological Obstructions -- 4.3. The Spin Group -- 4.4. Construction of Bundle Charts -- 4.5. Spin Structures -- Chapter 5. Further Examples -- 5.1. Compact Riemannian Spin Manifolds -- 5.2. Almost-Complex Structures on Riemannian Manifolds -- 5.3. Complex Structures on Riemannian Manifolds5.4. Kähler Structures -- Chapter 6. Tangent Cone Measures and the Tangential Clifford Section -- 6.1. The Tangent Cone Measure -- 6.2. Construction of a Tangential Clifford Section -- 6.3. Construction of a Spin Structure -- Chapter 7. The Topology of Discrete and Singular Fermion Systems -- Chapter 8. Basic Examples -- 8.1. The Euclidean Plane -- 8.2. Two-Dimensional Minkowski Space -- 8.3. The Euclidean Plane with Chiral Asymmetry -- 8.4. The Spin Structure of the Euclidean Plane with Chiral Asymmetry -- 8.5. The Spin Structure of Two-Dimensional Minkowski Space -- Chapter 9. Spinors on Singular Spaces9.1. Singularities of the Conformal Factor -- 9.2. Genuine Singularities of the Curvature Tensor -- 9.3. The Curvature Singularity of Schwarzschild Space-Time -- 9.4. A Lattice System with Non-Trivial Topology |
| Summary |
"Causal fermion systems and Riemannian fermion systems are proposed as aframework for describing non-smooth geometries. In particular, this framework pro-vides a setting for spinors on singular spaces. The underlying topological structuresare introduced and analyzed. The connection to the spin condition in differentialtopology is worked out. The constructions are illustrated by many simple exampleslike the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschildspace-time. As further examples, it is shown how complex and K ̈ahler structurescan be encoded in Riemannian fermion systems."--Page v |
| Notes |
"May 2019 - Volume 259 - Number 1251 (eighth of 8 numbers)." |
| Bibliography |
Includes bibliographical references (pages 81-83) |
| Notes |
Online resource; title from PDF title page (viewed August 27, 2019) |
| Subject |
Fermions.
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Geometry, Differential.
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Quantum theory.
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Quantum Theory
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Geometría diferencial
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Quanta, Teoría de los
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Fermions
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Geometry, Differential
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Quantum theory
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| Form |
Electronic book
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| Author |
Kamran, Niky, 1959- author.
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| ISBN |
9781470452575 |
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147045257X |
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1470436213 |
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9781470436216 |
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