Borrow it
Coverart for item
The Resource Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory, Olav Arnfinn Laudal

Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory, Olav Arnfinn Laudal

Creator
Summary
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 derivation. The book starts with a new definition of time, relative to which the set of mathematical velocities form a compact set, implying special and general relativity. With this model in mind, a general Quantum Theory is developed and shown to fit with the classical theory. In particular the "toy"--Model used as example, contains, as part of the structure, the classical gauge groups u(1), su(2) and su(3), and therefore also the theory of spin and quarks, etc
Language
eng
Work
Publication
Extent
1 online resource (x, 143 pages)
Contents
  • 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
Isbn
9789814343350
Instance
Label
Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory
Title
Geometry of time-spaces
Title remainder
non-commutative algebraic geometry, applied to quantum theory
Statement of responsibility
Olav Arnfinn Laudal
Creator
Subject
Language
eng
Summary
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 derivation. The book starts with a new definition of time, relative to which the set of mathematical velocities form a compact set, implying special and general relativity. With this model in mind, a general Quantum Theory is developed and shown to fit with the classical theory. In particular the "toy"--Model used as example, contains, as part of the structure, the classical gauge groups u(1), su(2) and su(3), and therefore also the theory of spin and quarks, etc
Cataloging source
N$T
http://library.link/vocab/creatorName
Laudal, Olav Arnfinn
Dewey number
530.15635
Illustrations
illustrations
Index
index present
LC call number
QC20.7.A37
LC item number
L38 2011eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Geometry, Algebraic
  • Noncommutative differential geometry
  • Quantum theory
  • SCIENCE
  • Geometry, Algebraic
  • Noncommutative differential geometry
  • Quantum theory
  • Géométrie algébrique
  • Géométrie différentielle non commutative
  • Théorie quantique
Label
Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory, Olav Arnfinn Laudal
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 137-143) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
754794363
Dimensions
unknown
Extent
1 online resource (x, 143 pages)
File format
unknown
Form of item
online
Isbn
9789814343350
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)754794363
Label
Geometry of time-spaces : non-commutative algebraic geometry, applied to quantum theory, Olav Arnfinn Laudal
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 137-143) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
754794363
Dimensions
unknown
Extent
1 online resource (x, 143 pages)
File format
unknown
Form of item
online
Isbn
9789814343350
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)754794363

Subject

Library Locations

    • Thomas Jefferson LibraryBorrow it
      1 University Blvd, St. Louis, MO, 63121, US
      38.710138 -90.311107

Library Links

Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Missouri-St. Louis Libraries. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...