Author | Das, Anadijiban. author |
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Title | The Special Theory of Relativity [electronic resource] : A Mathematical Exposition / by Anadijiban Das |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0893-8 |
Descript | XII, 232 p. online resource |
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 ร ? -- 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-ยฝ Fields in the Extended Phase Space -- Answers and Hints to Selected Exercises -- Index of Symbols