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Mathematical structures of the Universe /
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Kraków :
Copernicus Center Press,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Mathematical Structures of the Universe; Table of Contents; Introduction; Part I. General Relativity and Cosmology; Observer dependent geometries; 1. Geometry for observers and observables; 2. Geometry of the clock postulate: Finsler spacetimes; 2.1. De˝nition of Finsler spacetimes; 2.2. Causal structure and observers; 2.3. Dynamics for point masses; 2.4. Observers and observations; 2.5. Field theory; 2.6. Gravity; 3. The local perspective: Cartan geometry of observer space; 3.1. Definition of observer space; 3.2. Introduction to Cartan geometry; 3.3. Cartan geometry of observer space
- 3.4. Observers and observations3.5. Gravity; 3.6. The role of spacetime; Acknowledgments; References; Classification of classical singularities: a differential spaces approach; 1. Motivation; 2. Fundamental concepts; 3. Spectral properties; 4. B-boundary; 5. Singularities; Acknowledgment; References; The smooth beginning of the Universe; 1. Introduction; 2. Sikorski's di˙erential spaces and GR; 3. A differential space for the flat FRW d-manifold; 4. Time orientability; 5. A smooth evolution with respect to cosmological time; 6. The simplest smoothly evolving models; 7. Interpretation
- 8. Smoothly evolved models in a neighbourhood of singularity9. Summary; Acknowledgments; References; Are singularities the limits of cosmology?; 1. What are singularities?; 2. Big-Bang and non-Big-Bang singularities in cosmology; 2.1. The strength of singularities; 2.2. Geodesics and geodesic deviation; 2.3. Spacetime averaging; 2.4. Energy conditions; 3. Properties and classification of singularities; 4. Varying constants removing or changing singularities; 4.1. Removing a Big-Bang singularity
- VG; 4.2. Removing SFS or FSF
- VSL; 4.3. Removing SFS or FSF
- VG; 4.4. A hybrid case
- VG
- Two-body problem in General RelativitySummary; Acknowledgments; References; Part II. Quantum Geometries; Geometry of quantum correlations; 1. Introduction; 2. The geometry of quantum mechanics; 3. A symplectic setting for classical mechanics; 4. Classical Hamiltonian systems with symmetry; 5. Symplectic structures in spaces of quantum states; 6. Composite quantum systems; separable and entangled states; 7. Quantum correlations and symplectic geometry; 7.1. Symplectic measures of entanglement; 7.2. Local unitary equivalence of states