Theory Of Relativity

Theory Of Relativity

Hardcover

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Product Details

ISBN-13: 9789814641890
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 03/30/2015
Pages: 228
Product dimensions: 5.93(w) x 9.25(h) x 0.56(d)

Table of Contents

Preface vii

Special Theory of Relativity 1

1 Galilean Transformations 3

1.1 Introduction 3

1.2 Galilean Transformations 4

1.3 Newtonian Mechanics and the Principle of Galilean Relativity 5

1.3.1 Electrodynamics and Galilean Relativity 6

2 Lorentz Transformations 9

2.1 The Two Postulates of Relativity 9

2.2 Lorentz-Fitz Gerald Contraction 12

2.3 Time Dilation 13

2.4 Proper Time 15

2.5 Transformation of Particle Velocities 16

3 Relativistic Mechanics 17

3.1 Momentum and Energy 17

3.2 Application of Relativistic Mechanics 22

3.2.1 Doppler Shift 22

3.3 Scattering Kinematics 23

3.3.1 Two-Particle Scattering 23

3.4 Motion of a Charged Particle in a Uniform Magnetic Field 27

3.5 Problems Related to Chapters 2 and 3 30

4 Loitentz Transformations (General Case) 39

4.1 Lorentz Transformations (General Case) (in Four Dimensional Space Time) 39

4.2 Light Cone 43

4.3 Lorentz Boost Transformation 44

4.4 Vectors and Tensors 45

5 Four-Velocity: Minkowski Force 49

5.1 Four-Velocity 49

5.2 Minkowski Force 50

5.3 Problems 53

6 Covariant Form Of Electrodynamics 55

6.1 Electromagnetic Field Tensor 55

6.1.1 Lorentz Force 57

6.2 Transformation of E and B Under Lorentz Transformation 59

6.3 Electromagnetic Field of a Moving Charge 60

6.4 Scalar and Vector Potential of a Moving Charge 61

6.5 Covariant Form of Maxwell's Equations 62

6.6 Energy-Momentum Tensor of an Electromagnetic Field 63

6.7 Problems 65

7 Spin 71

7.1 Relativistic Equations of Motion for Spin in a Uniform External Electromagnetic Field 71

7.2 Problem 75

8 Space Time Groups and their Representations 77

8.1 Matrix Representation of Lorent-z Transformation 77

8.2 Invariance: Representations of a Group 80

8.3 Poincaré Group and its Representations 82

8.4 Poincaré Group and Physical States 93

8.5 Scale Invariance 97

8.5.1 Scale Transformation 98

8.5.2 Conformal Group 99

8.6 Energy Momentum Tensor 101

8.7 Super-symmetry (SUSY) 103

8.8 SUSY Quantum Mechanics 105

8.8.1 SUSY Vacuum 107

8.9 Super Lie Algebra 107

8.9.1 Two-component Spinors 109

8.9.2 Spinor Charges 112

8.10 Super symmetric Multiplets 116

8.11 Problems 120

General Theory of Relativity: Riemannian Geometry; Curved Space Time 131

9 Tensor Analysis and Affine Connection 133

9.1 Introduction 133

9.2 Metric Tensor, Tensors, Tensor Densities 134

9.2.1 Tensors. Tensor Densities 136

9.3 Covariant Derivative, Affine Connection, Christoffel Symbol 139

9.4 Gradient, Curl and Divergence 145

9.5 Problems 146

10 Geodesic and Equivalence Principle 151

10.1 Geodesic Equation 151

10.2 Equivalence Principle 153

10.3 Weak Field and Low Velocity Limit: Gravity as a Metric Phenomenon 155

10.4 Problems 158

11 Curvature Tensor and Einstein's Field Equations 161

11.1 Curvature Tensor 161

11.2 Einstein's Field Equations 165

11.3 Newtonian Limit of Field Equations 167

11.4 Problems 168

12 The Schwarzsohild, Friedmann Robertson Walker Metric 173

12.1 Introduction 173

12.2 The Schwarzschild Metric 174

12.3 Friedmannn-Robertson-Walker (FRW) Metric 178

12.4 Cosmology ISO

12.4.1 Cosmological Principle ISO

12.4.2 Standard Model of Cosmology 182

12.4.3 Friedmann-Lemaitre Equations 184

12.4.4 Observational Cosmology 186

12.5 Problems 191

Appendix 199

A.1 Covariant Derivative; Parallel Displacement of a Vector 199

A.2 Hot Big Bang: Thermal History of the Universe 201

A.2.1 Thermal Equilibrium 201

A.2.2 The Radiation Era 203

A.3 Fundamental Units 208

Bibliography 213

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