Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory /
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| Author / Creator: | Laudal, Olav Arnfinn. |
|---|---|
| Imprint: | Singapore ; Hackensack, N.J. : World Scientific, c2011. |
| Description: | x, 143 p. : ill. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8437489 |
Table of Contents:
- Preface
- 1. Introduction
- 1.1. Philosophy
- 1.2. Phase Spaces, and the Dirac Derivation
- 1.3. Non-commutative Algebraic Geometry, and Moduli of Simple Modules
- 1.4. Dynamical Structures
- 1.5. Quantum Fields and Dynamics
- 1.6. Classical Quantum Theory
- 1.7. Planck's Constants, and Fock Space
- 1.8. General Quantum Fields, Lagrangians and Actions
- 1.9. Grand Picture. Bosons, Fermions, and Supersymmetry
- 1.10. Connections and the Generic Dynamical Structure
- 1.11. Clocks and Classical Dynamics
- 1.12. Time-Space and Space-Times
- 1.13. Cosmology, Big Bang and All That
- 1.14. Interaction and Non-commutative Algebraic Geometry
- 1.15. Apology
- 2. Phase Spaces and the Dirac Derivation
- 2.1. Phase Spaces
- 2.2. The Dirac Derivation
- 3. Non-commutative Deformations and the Structure of the Moduli Space of Simple Representations
- 3.1. Non-commutative Deformations
- 3.2. The O-construction
- 3.3. Iterated Extensions
- 3.4. Non-commutative Schemes
- 3.4.1. Localization, Topology and the Scheme Structure on Simp(A)
- 3.4.2. Completions of Simp n (A)
- 3.5. Morphisms, Hilbert Schemes, Fields and Strings
- 4. Geometry of Time-spaces and the General Dynamical Law
- 4.1. Dynamical Structures
- 4.2. Quantum Fields and Dynamics
- 4.3. Classical Quantum Theory
- 4.4. Planck's Constant(s) and Fock Space
- 4.5. General Quantum Fields, Lagrangians and Actions
- 4.6. Grand Picture: Bosons, Fermions, and Supersymmetry
- 4.7. Connections and the Generic Dynamical Structure
- 4.8. Clocks and Classical Dynamics
- 4.9. Time-space and Space-times
- 4.10. Cosmology, Big Bang and All That
- 5. Interaction and Non-commutative Algebraic Geometry
- 5.1. Interactions
- 5.2. Examples and Some Ideas
- Bibliography
- Index
