The Special Theory of Relativity

1. Four-Dimensional Vector Spaces and Linear Mappings.- 1.1. Minkowski Vector Space V4.- 1.2. Lorentz Mappings of V4.- 1.3. The Minkowski Tensors.- 2. Flat Minkowski Space-Time Manifold M4 and Tensor Fields.- 2.1. A Four-Dimensional Differentiable Manifold.- 2.2. Minkowski Space-Time M4 and the Separation Function.- 2.3. Flat Submanifolds of Minkowski Space-Time M4.- 2.4. Minkowski Tensor Fields on M4.- 3. The Lorentz Transformation.- 3.1. Applications of the Lorentz Transformation.- 3.2. The Lorentz Group ?4.- 3.3. Real Representations of the Lorentz Group ?4.- 3.4. The Lie Group ?+4+.- 4. Pauli Matrices, Spinors, Dirac Matrices, and Dirac Bispinors.- 4.1. Pauli Matrices, Rotations, and Lorentz Transformations.- 4.2. Spinors and Spinor-Tensors.- 4.3. Dirac Matrices and Dirac Bispinors.- 5. The Special Relativistic Mechanics.- 5.1. The Prerelativistic Particle Mechanics.- 5.2. Prerelativistic Particle Mechanics in Space and Time E3 × ?.- 5.3. The Relativistic Equation of Motion of a Particle.- 5.4. The Relativistic Lagrangian and Hamiltonian Mechanics of a Particle.- 6. The Special Relativistic Classical Field Theory.- 6.1. Variational Formalism for Relativistic Classical Fields.- 6.2. The Klein-Gordon Scalar Field.- 6.3. The Electromagnetic Tensor Field.- 6.4. Nonabelian Gauge Fields.- 6.5. The Dirac Bispinor Field.- 6.6. Interaction of the Dirac Field with Gauge Fields.- 7. The Extended (or Covariant) Phase Space and Classical Fields.- 7.1. Classical Fields.- 7.2. The Generalized Klein-Gordon Equation.- 7.3. Spin-½ Fields in the Extended Phase Space.- Answers and Hints to Selected Exercises.- Index of Symbols.