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Chapter1.Four-Dimensional Vector Spaces and Linear Mappings 1

1.1.Minkowski Vector Space V4 1

1.2.Lorentz Mappings of V4 8

1.3.The Minkowski Tensors 13

Chapter2.Flat Minkowski Space-Time Manifold M4 and Tensor Fields 20

2.1.A Four-Dimensional Differentiable Manifold 20

2.2.Minkowski Space-Time M4 and the Separation Function 25

2.3.Flat Submanifolds of Minkowski Space-Time M4 35

2.4.Minkowski Tensor Fields on M4 41

Chapter3.The Lorentz Transformation 48

3.1.Applications of the Lorentz Transformation 48

3.2.The Lorentz Group ?4 55

3.3.Real Representations of the Lorentz Group ?4 59

3.4.The Lie Group ?+4+ 63

Chapter4.Pauli Matrices，Spinors，Dirac Matrices，and Dirac Bispinors 72

4.1.Pauli Matrices，Rotations，and Lorentz Transformations 72

4.2.Spinors and Spinor-Tensors 79

4.3.Dirac Matrices and Dirac Bispinors 85

Chapter5.The Special Relativistic Mechanics 89

5.1.The Prerelativistic Particle Mechanics 89

5.2.Prerelativistic Particle Mechanics in Space and Time E3×R 95

5.3.The Relativistic Equation of Motion of a Particle 100

5.4.The Relativistic Lagrangian and Hamiltonian Mechanics of a Particle 108

Chapter6.The Special Relativistic Classical Field Theory 120

6.1.Variational Formalism for Relativistic Classical Fields 120

6.2.The Klein-Gordon Scalar Field 133

6.3.The Electromagnetic Tensor Field 140

6.4.Nonabelian Gauge Fields 147

6.5.The Dirac Bispinor Field 151

6.6.Interaction of the Dirac Field with Gauge Fields 160

Chapter7.The Extended(or Covariant)Phase Space and Classical Fields 168

7.1.Classical Fields 168

7.2.The Generalized Klein-Gordon Equation 175

7.3.Spin-1/2 Fields in the Extended Phase Space 190

Answers and Hints to Selected Exercises 202

Index of Symbols 204

Subject Index 207