Indicting the 45th President (Crimes of the Powerful)

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
		2.2.3. The Galilean Relativity Principle
		2.2.4. A Trouble with the Galilean Space-Time
	2.3. Newtonian Space-Times
		2.3.1. Definitions
		2.3.2. Gravitational Field
		2.3.3. A Trouble with Newtonian Space-Times
	2.4. The Minkowskian Spacetime
		2.4.1. Basic Definitions
		2.4.2. The Einstein Relativity Principle
		2.4.3. The Energy-Momentum Tensor
		2.4.4. Neutrino Field
		2.4.5. Electromagnetic Field
		2.4.6. A Trouble with Minkowskian Spacetime
	2.5. Einsteinian Spacetimes
		2.5.1. Notation
		2.5.2. Gravitational Field
		2.5.3. The Robertson–Walker Metric
		2.5.4. The Friedman Equations
	2.6. Relativistic Wave Equations on the Minkowskian Spacetime
		2.6.1. A Transition to an Equivalent Representation
		2.6.2. Relativistic Wave Equations in the Frequency-Wave-Number Domain
		2.6.3. A Transition to the Space Domain
	2.7. Neutrino, Electromagnetic, and Gravitational Waves
		2.7.1. Relativistic Wave Equations on Einstein Spacetimes
		2.7.2. The Geometrical Optics Approximation
		2.7.3. Polarisation
	2.8. Bibliographical Remarks
3. Random Cross-Sections of Homogeneous Bundles
	3.1. Isotropic Random Cross-Sections
	3.2. Examples of Special Bases: The Irreducible Case
	3.3. Physical Application of the Irreducible Case
	3.4. Examples of Special Bases: The Reducible Case
		3.4.1. The Polarisation Matrix
		3.4.2. Vector and Tensor Spherical Harmonics
		3.4.3. The Bases
	3.5. Physical Application of the Reducible Case
	3.6. Concluding Remarks: Where to Go Next?
	3.7. Bibliographical Remarks
A. Additional Topics
	A.1. Commutative Diagrams
	A.2. Categories
	A.3. Universality
		A.3.1. Initial and Terminal Objects
		A.3.2. Comma Categories
		A.3.3. Universal Objects and Universal Maps
		A.3.4. Adjoint and Coadjoint Functors
	A.4. Spin Manifolds
	A.5. Bibliographical Remarks
Bibliography
Index