Probabilistic models of cosmic backgrounds

• Verfasst von: Malyarenko, Anatoliy [VerfasserIn]
• Titel: Probabilistic models of cosmic backgrounds
• Verf.angabe: Anatoliy Malyarenko
• Ausgabe: First edition
• Verlagsort: Boca Raton ; London ; New York
• Verlag: CRC Press, Taylor & Francis Group
• Jahr: 2024
• Umfang: 1 Online-Ressource (xxvii, 259 Seiten)
• Fussnoten: Description based on publisher supplied metadata and other sources
• ISBN: 978-1-04-002127-9
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Malyarenko, Anatoliy: Probabilistic models of cosmic backgrounds. - First edition. - Boca Raton, FL : CRC Press/Taylor & Francis Group, 2024. - xxvii, 259 pages
• K10plus-PPN: 1884917518
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Foreword -- Preface -- Acknowledgements -- List of Figures -- List of Tables -- List of Symbols -- 1. Mathematical Preliminaries -- 1.1. Skew Fields -- 1.2. Linear Spaces -- 1.2.1. Notation -- 1.2.2. Operations over Linear Spaces -- 1.2.3. Additional Structures on Complex Linear Spaces -- 1.3. Algebras -- 1.3.1. Definitions -- 1.3.2. Representations of Algebras -- 1.3.3. Clifford Algebras -- 1.3.4. Examples of Clifford Algebras in Low Dimensions -- 1.3.5. Clifford Involutions -- 1.4. Algebraic Spinors -- 1.5. Manifolds and Coverings -- 1.5.1. Manifolds -- 1.5.2. Coverings -- 1.6. Lie Groups -- 1.7. Vector and Tensor Fields -- 1.7.1. Bundles: A Group Action Approach -- 1.7.2. Bundles: A Classical Approach -- 1.7.3. Bundles: A Cocycle Approach -- 1.7.4. Riemannian Manifolds and Geodesics -- 1.7.5. The Riemannian Measure -- 1.7.6. Differentiation of Vector and Tensor Fields -- 1.7.7. Isometries -- 1.8. Group Representations -- 1.8.1. Basic Definitions -- 1.8.2. Operations over Representations -- 1.8.3. Integration and Characters -- 1.8.4. The Adams Notation -- 1.8.5. Classical Spinors -- 1.8.6. Spin-Tensors -- 1.8.7. The Clebsch-Gordan Decomposition -- 1.9. Spin and Spin-Tensor Fields -- 1.9.1. Spin Bundles: A Group Action Approach -- 1.9.2. Spin Bundles: A Classical Approach -- 1.9.3. Spin Bundles: A Cocycle Approach -- 1.9.4. Differentiation of Spin Fields -- 1.10. Induced Representations -- 1.11. Probability -- 1.11.1. Random Elements -- 1.11.2. Random Cross-Sections -- 1.12. Bibliographical Remarks -- 2. Space-Times and Spacetimes -- 2.1. The Aristotelian Space-Time -- 2.1.1. The Description by Penrose -- 2.1.2. The Modification by Ptolemy -- 2.2. The Galilean Space-Time -- 2.2.1. Coordinate-Free Definitions -- 2.2.2. Introducing Coordinates.

Abstract

"Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard to find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories"--