Author | Woodhouse, Nicholas M. J. author |
---|---|
Title | Special Relativity [electronic resource] / by Nicholas M. J. Woodhouse |
Imprint | London : Springer London : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0083-6 |
Descript | X, 196 p. online resource |
1. Relativity in Classical Mechanics -- 1.1 Frames of Reference -- 1.2 Relativity -- 1.3 Frames of Reference -- 1.4 Newtonโs Laws -- 1.5 Galilean Transformations -- 1.6 Mass, Energy, and Momentum -- 1.7 Space-time -- 1.8 *Galilean Symmetries -- 1.9 Historical Note -- 2. Maxwellโs Theory -- 2.1 Introduction -- 2.2 The Unification of Electricity and Magnetism -- 2.3 Charges, Fields, and the Lorentz Force Law -- 2.4 Stationary Distributions of Charge -- 2.5 The Divergence of the Magnetic Field -- 2.6 Inconsistency with Galilean Relativity -- 2.7 The Limits of Galilean Invariance -- 2.8 Faradayโs Law of Induction -- 2.9 The Field of Charges in Uniform Motion -- 2.10 Maxwellโs Equations -- 2.11 The Continuity Equation -- 2.12 Conservation of Charge -- 2.13 Historical Note -- 3. The Propagation of Light -- 3.1 The Displacement Current -- 3.2 The Source-free Equations -- 3.3 The Wave Equation -- 3.4 Monochromatic Plane Waves -- 3.5 Polarization -- 3.6 Potentials -- 3.7 Gauge Transformations -- 3.8 Photons -- 3.9 Relativity and the Propagation of Light -- 3.10 The Michelson-Morley Experiment -- 4. Einsteinโs Special Theory of Relativity -- 4.1 Lorentzโs Contraction -- 4.2 Operational Definitions of Distance and Time -- 4.3 The Relativity of Simultaneity -- 4.4 Bondiโs fc-Factor -- 4.5 Time Dilation -- 4.6 The Two-dimensional Lorentz Transformation -- 4.7 Transformation of Velocity -- 4.8 The Lorentz Contraction -- 4.9 Composition of Lorentz Transformations -- 4.10 Rapidity -- 4.11 *The Lorentz and Poincarรฉ Groups -- 5. Lorentz Transformations in Four Dimensions -- 5.1 Coordinates in Four Dimensions -- 5.2 Four-dimensional Coordinate Transformations -- 5.3 The Lorentz Transformation in Four Dimensions -- 5.4 The Standard Lorentz Transformation -- 5.5 The General Lorentz Transformation -- 5.6 Euclidean Space and Minkowski Space -- 5.7 Four-vectors -- 5.8 Temporal and Spatial Parts -- 5.9 The Inner Product -- 5.10 Classification of Four-vectors -- 5.11 Causal Structure of Minkowski Space -- 5.12 Invariant Operators -- 5.13 The Frequency Four-vector -- 5.14 * Affine Spaces and Covectors -- 6. Relative Motion -- 6.1 Transformations Between Frames -- 6.2 Proper Time -- 6.3 Four-velocity -- 6.4 Four-acceleration -- 6.5 Constant Acceleration -- 6.6 Continuous Distributions -- 6.7 *Rigid Body Motion -- 6.8 Visual Observation -- 7. Relativistic Collisions -- 7.1 The Operational Definition of Mass -- 7.2 Conservation of Four-momentum -- 7.3 Equivalence of Mass and Energy -- 8. Relativistic Electrodynamics -- 8.1 Lorentz Transformations of E and B -- 8.2 The Four-Current and the Four-potential -- 8.3 Transformations of E and B -- 8.4 Linearly Polarized Plane Waves -- 8.5 Electromagnetic Energy -- 8.6 The Four-momentum of a Photon -- 8.7 *Advanced and Retarded Solutions -- 9. *Tensors and Isomet ries -- 9.1 Affine Space -- 9.2 The Lorentz Group -- 9.3 Tensors -- 9.4 The Tensor Product -- 9.5 Tensors in Minkowski Space -- 9.6 Tensor Components -- 9.7 Examples of Tensors -- 9.8 One-parameter Subgroups -- 9.9 Isometries -- 9.10 The Riemann Sphere and Spinors -- Notes on Exercises -- Vector Calculus