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Mathematical Models In Science [Kietas viršelis]

(Univ Of Oslo, Norway)
  • Formatas: Hardback, 320 pages
  • Išleidimo metai: 28-Jun-2021
  • Leidėjas: World Scientific Europe Ltd
  • ISBN-10: 1800610270
  • ISBN-13: 9781800610279
Kitos knygos pagal šią temą:
Mathematical Models In ScienceDidesnis paveikslėlis
  • Formatas: Hardback, 320 pages
  • Išleidimo metai: 28-Jun-2021
  • Leidėjas: World Scientific Europe Ltd
  • ISBN-10: 1800610270
  • ISBN-13: 9781800610279
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781800610279.html
Raktažodžiai:
Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.
Acknowledgment vii
1 Introduction 1(12)
1.1 Philosophy
1(3)
1.2 Mathematical Models
4(2)
1.3 Geometry of the Space of Models
6(2)
1.4 Cosmology
8(1)
1.5 Organization of the Work: Leitfaden
9(4)
2 Dynamics 13(26)
2.1 The Phase Space Functor
13(9)
2.1.1 First properties
14(3)
2.1.2 The deformation functor of representations
17(2)
2.1.3 Blow-ups and desingularizations
19(3)
2.1.4 Chern classes
22(1)
2.2 The Iterated Phase Space Functor Ph* and the Dirac Derivation
22(9)
2.2.1 Formal curves of representations
30(1)
2.3 The Generalized de Rham Complex
31(8)
2.3.1 Excursion into the Jacobian conjecture
36(3)
3 Non-Commutative Algebraic Geometry 39(14)
3.1 Moduli of Representations
40(1)
3.2 Moduli of Simple Modules
41(3)
3.2.1 Evolution in the moduli of simple modules
42(2)
3.3 Non-Commutative Deformations of Swarms
44(9)
4 The Dirac Derivation and Dynamical Structures 53(56)
4.1 Dynamical Structures
53(4)
4.2 Gauge Groups and Invariant Theory
57(7)
4.2.1 The global gauge group and invariant theory
57(3)
4.2.2 The local gauge group
60(4)
4.3 The Generic Dynamical Structures Associated to a Metric
64(5)
4.3.1 The commutative case, metrics, and gravitation
64(3)
4.3.2 The Lie algebra of isometries
67(2)
4.4 Metrics, Gravitation, and Energy
69(13)
4.4.1 The case of subspaces, spectral triples
79(2)
4.4.2 Relations to Clifford algebras
81(1)
4.5 Potentials and the Classical Gauge Invariance
82(6)
4.5.1 Infinitesimal structure on Rep(C(σg))
83(3)
4.5.2 Physics and the Chern-Simons class
86(2)
4.6 A Generalized Yang-Mills Theory
88(7)
4.7 Reuniting GR, YM, and General QFT
95(10)
4.8 Family of Representations versus Family of Metrics
105(4)
5 Time-Space and Space-Times 109(24)
5.1 The Cylindrical Coordinates, Newton, and Kepler
111(12)
5.2 Thermodynamics, the Heat Equation and Navier-Stokes
123(10)
6 Entropy 133(14)
6.1 The Classical Commutative Case
133(1)
6.2 The General Case
134(3)
6.3 Representations of Phinfinity
137(10)
7 Cosmology, Cosmos, and Cosmological Time 147(24)
7.1 Background, and Some Remarks on Philosophy of Science
147(3)
7.2 Deformations of Associative Algebras
150(6)
7.3 The Universal Gauge Groups and SUSY
156(9)
7.4 The Singular Sub-Scheme of SUSY
165(6)
8 The Universe as a Versal Base Space 171(16)
8.1 First Properties
172(5)
8.2 Density of Mass, Inflation, and Cyclical Cosmology
177(2)
8.3 A Conformally Trivial Cosmological Model
179(3)
8.4 Where Are We, the Observers, in This Universe?
182(3)
8.5 The Speed of Photons, and the Red-Shift
185(2)
9 Worked Out Formulas 187(16)
9.1 Some Examples
187(2)
9.2 Action of g, and a Canonical Basis for Vector Fields
189(3)
9.3 The 8-Fold Way of Gell-Mann: The "Real" Story
192(7)
9.3.1 Charge, and the charge conjugation operator C
197(2)
9.4 Adjoint Actions of g
199(4)
10 Summing Up the Model 203(40)
10.1 Metrics, Particles, and the Furniture
205(6)
10.2 Time, Gravitation, and Einstein's Equation
211(7)
10.2.1 Einsteins field equations
214(4)
10.3 Energy, Dirac, and Maxwell
218(16)
10.3.1 Energy
219(3)
10.3.2 Dirac
222(3)
10.3.3 Classical Maxwell equations
225(5)
10.3.4 Photons, tenebrous, and electrons
230(4)
10.4 Black Mass and Energy
234(4)
10.5 Ensembles, Bi-Algebras, and Quantum Groups
238(4)
10.6 Black Mass and Gravitational "Waves"
242(1)
11 Particles, Fields, and Probabilities 243(10)
11.1 Elementary Particles
244(4)
11.2 Time as a Source for Probabilities
248(2)
11.3 Quantum Field Theory, Wightman's Axioms
250(3)
12 Interactions 253(22)
12.1 Interaction and Non-Commutative Deformations
254(1)
12.2 The Weak and Strong Interactions
255(11)
12.3 Graphs and Sub-Categories Generated by a Family of Modules
266(4)
12.3.1 Interactions and dynamics
268(2)
12.4 Creating New Particles from Old Ones
270(2)
12.5 Entanglement, Consciousness
272(13)
12.5.1 Self-reflection
273(2)
13 Comparing the Toy Model with the Standard Model 275(10)
14 End Words 285(14)
14.1 Relations to Non-Commutative Geometry (NCG)
287(2)
14.2 Models for Quantum Gravitation
289(1)
14.3 The General Dynamical Model
290(2)
14.4 Time, Lagrangians, Probabilities, Reality
292(5)
14.4.1 Unsolved problems in physics
294(1)
14.5 Relations to Classical Cosmologies
295(2)
14.6 So What?
297(2)
Bibliography 299(4)
Index 303