Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory /

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory of phase spaces, and its canonical Dirac deriv...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Laudal, Olav Arnfinn
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific, ©2011.
Temas:
Geometry, Algebraic.
Noncommutative differential geometry.
Quantum theory.
Quantum Theory
Géométrie algébrique.
Géométrie différentielle non commutative.
Théorie quantique.
SCIENCE > Physics > Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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. 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.

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