دانلود کتاب Mathematical Models in Science

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Contents
Acknowledgment
1. Introduction
1.1 Philosophy
1.2 Mathematical Models
1.3 Geometry of the Space of Models
1.4 Cosmology
1.5 Organization of the Work: Leitfaden
2. Dynamics
2.1 The Phase Space Functor
2.1.1 First properties
2.1.2 The deformation functor of representations
2.1.3 Blow-ups and desingularizations
2.1.4 Chern classes
2.2 The Iterated Phase Space Functor Ph∗ and the Dirac Derivation
2.2.1 Formal curves of representations
2.3 The Generalized de Rham Complex
2.3.1 Excursion into the Jacobian conjecture
3. Non-Commutative Algebraic Geometry
3.1 Moduli of Representations
3.2 Moduli of Simple Modules
3.2.1 Evolution in the moduli of simple modules
3.3 Non-Commutative Deformations of Swarms
4. The Dirac Derivation and Dynamical Structures
4.1 Dynamical Structures
4.2 Gauge Groups and Invariant Theory
4.2.1 The global gauge group and invariant theory
4.2.2 The local gauge group
4.3 The Generic Dynamical Structures Associated to a Metric
4.3.1 The commutative case, metrics, and gravitation
4.3.2 The Lie algebra of isometries
4.4 Metrics, Gravitation, and Energy
4.4.1 The case of subspaces, spectral triples
4.4.2 Relations to Clifford algebras
4.5 Potentials and the Classical Gauge Invariance
4.5.1 Infinitesimal structure on Rep(C(σg))
4.5.2 Physics and the Chern–Simons class
4.6 A Generalized Yang–Mills Theory
4.7 Reuniting GR, YM, and General QFT
4.8 Family of Representations versus Family of Metrics
5. Time–Space and Space–Times
5.1 The Cylindrical Coordinates, Newton, and Kepler
5.2 Thermodynamics, the Heat Equation and Navier–Stokes
6. Entropy
6.1 The Classical Commutative Case
6.2 The General Case
6.3 Representations of Ph∞
7. Cosmology, Cosmos, and Cosmological Time
7.1 Background, and Some Remarks on Philosophy of Science
7.2 Deformations of Associative Algebras
7.3 The Universal Gauge Groups and SUSY
7.4 The Singular Sub-Scheme of SUSY
8. The Universe as a Versal Base Space
8.1 First Properties
8.2 Density of Mass, Inflation, and Cyclical Cosmology
8.3 A Conformally Trivial Cosmological Model
8.4 Where Are We, the Observers, in This Universe?
8.5 The Speed of Photons, and the Red-Shift
9. Worked Out Formulas
9.1 Some Examples
9.2 Action of g, and a Canonical Basis for Vector Fields
9.3 The 8-Fold Way of Gell-Mann: The “Real” Story
9.3.1 Charge, and the charge conjugation operator C
9.4 Adjoint Actions of g
10. Summing Up the Model
10.1 Metrics, Particles, and the Furniture
10.2 Time, Gravitation, and Einstein’s Equation
10.2.1 Einsteins field equations
10.3 Energy, Dirac, and Maxwell
10.3.1 Energy
10.3.2 Dirac
10.3.3 Classical Maxwell equations
10.3.4 Photons, tenebrons, and electrons
10.4 Black Mass and Energy
10.5 Ensembles, Bi-Algebras, and Quantum Groups
10.6 Black Mass and Gravitational “Waves”
11. Particles, Fields, and Probabilities
11.1 Elementary Particles
11.2 Time as a Source for Probabilities
11.3 Quantum Field Theory, Wightman’s Axioms
12. Interactions
12.1 Interaction and Non-Commutative Deformations
12.2 The Weak and Strong Interactions
12.3 Graphs and Sub-Categories Generated by a Family of Modules
12.3.1 Interactions and dynamics
12.4 Creating New Particles from Old Ones
12.5 Entanglement, Consciousness
12.5.1 Self-reflection
13. Comparing the Toy Model with the Standard Model
14. End Words
14.1 Relations to Non-Commutative Geometry (NCG)
14.2 Models for Quantum Gravitation
14.3 The General Dynamical Model
14.4 Time, Lagrangians, Probabilities, Reality
14.4.1 Unsolved problems in physics
14.5 Relations to Classical Cosmologies
14.6 So What?
Bibliography
Index