Spinors on singular spaces and the topology of causal fermion systems /

"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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Finster, Felix, 1967- (Autor), Kamran, Niky, 1959- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, 2019.
Colección:Memoirs of the American Mathematical Society ; no. 1251.
Temas:
Fermions.
Geometry, Differential.
Quantum theory.
Quantum Theory
Géométrie différentielle.
Théorie quantique.
Geometría diferencial
Quanta, Teoría de los
Fermions
Geometry, Differential
Quantum theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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

Ejemplares similares