《狭义相对论的数学表述》

Chapter1.Four-Dimensional Vector Spaces and Linear Mappings1

1.1.Minkowski Vector Space V41

1.2.Lorentz Mappings of V48

1.3.The Minkowski Tensors13

Chapter2.Flat Minkowski Space-Time Manifold M4 and Tensor Fields20

2.1.A Four-Dimensional Differentiable Manifold20

2.2.Minkowski Space-Time M4 and the Separation Function25

2.3.Flat Submanifolds of Minkowski Space-Time M435

2.4.Minkowski Tensor Fields on M441

Chapter3.The Lorentz Transformation48

3.1.Applications of the Lorentz Transformation48

3.2.The Lorentz Group ?455

3.3.Real Representations of the Lorentz Group ?459

3.4.The Lie Group ?+4+63

Chapter4.Pauli Matrices，Spinors，Dirac Matrices，and Dirac Bispinors72

4.1.Pauli Matrices，Rotations，and Lorentz Transformations72

4.2.Spinors and Spinor-Tensors79

4.3.Dirac Matrices and Dirac Bispinors85

Chapter5.The Special Relativistic Mechanics89

5.1.The Prerelativistic Particle Mechanics89

5.2.Prerelativistic Particle Mechanics in Space and Time E3×R95

5.3.The Relativistic Equation of Motion of a Particle100

5.4.The Relativistic Lagrangian and Hamiltonian Mechanics of a Particle108

Chapter6.The Special Relativistic Classical Field Theory120

6.1.Variational Formalism for Relativistic Classical Fields120

6.2.The Klein-Gordon Scalar Field133

6.3.The Electromagnetic Tensor Field140

6.4.Nonabelian Gauge Fields147

6.5.The Dirac Bispinor Field151

6.6.Interaction of the Dirac Field with Gauge Fields160

Chapter7.The Extended(or Covariant)Phase Space and Classical Fields168

7.1.Classical Fields168

7.2.The Generalized Klein-Gordon Equation175

7.3.Spin-1/2 Fields in the Extended Phase Space190

Answers and Hints to Selected Exercises202

Index of Symbols204

Subject Index207