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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

Hardcover Published: 22nd March 2011
ISBN: 9789814343343
Number Of Pages: 143

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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.

Prefacep. vii
Introductionp. 1
Philosophyp. 1
Phase Spaces, and the Dirac Derivationp. 3
Non-commutative Algebraic Geometry, and Moduli of Simple Modulesp. 4
Dynamical Structuresp. 5
Quantum Fields and Dynamicsp. 6
Classical Quantum Theoryp. 9
Planck's Constants, and Fock Spacep. 9
General Quantum Fields, Lagrangians and Actionsp. 10
Grand Picture. Bosons, Fermions, and Supersymmetryp. 12
Connections and the Generic Dynamical Structurep. 12
Clocks and Classical Dynamicsp. 13
Time-Space and Space-Timesp. 13
Cosmology, Big Bang and All Thatp. 14
Interaction and Non-commutative Algebraic Geometryp. 14
Apologyp. 15
Phase Spaces and the Dirac Derivationp. 17
Phase Spacesp. 17
The Dirac Derivationp. 22
Non-commutative Deformations and the Structure of the Moduli Space of Simple Representationsp. 27
Non-commutative Deformationsp. 27
The O-constructionp. 29
Iterated Extensionsp. 31
Non-commutative Schemesp. 32
Localization, Topology and the Scheme Structure on Simp(A)p. 33
Completions of Simpn(A)p. 42
Morphisms, Hilbert Schemes, Fields and Stringsp. 46
Geometry of Time-spaces and the General Dynamical Lawp. 51
Dynamical Structuresp. 51
Quantum Fields and Dynamicsp. 52
Classical Quantum Theoryp. 58
Planck's Constant(s) and Fock Spacep. 60
General Quantum Fields, Lagrangians and Actionsp. 64
Grand Picture: Bosons, Fermions, and Supersymmetryp. 69
Connections and the Generic Dynamical Structurep. 76
Clocks and Classical Dynamicsp. 102
Time-space and Space-timesp. 103
Cosmology, Big Bang and All Thatp. 120
Interaction and Non-commutative Algebraic Geometryp. 125
Interactionsp. 125
Examples and Some Ideasp. 128
Bibliographyp. 137
Indexp. 141
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789814343343
ISBN-10: 981434334X
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 143
Published: 22nd March 2011
Country of Publication: SG
Dimensions (cm): 23.11 x 15.49  x 1.52
Weight (kg): 0.43

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