Author | Parrott, Stephen. author |
---|---|
Title | Relativistic Electrodynamics and Differential Geometry [electronic resource] / by Stephen Parrott |
Imprint | New York, NY : Springer New York, 1987 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4684-8 |
Descript | XI, 308 p. online resource |
1. Special Relativity -- 1.1 Coordinatizations of spacetime -- 1.2 Lorentz coordinatizations -- 1.3 Minkowski space -- 1.4 Lorentz transformations -- 1.5 Orientations -- 1.6 Spacetime diagrams and the metric tensor -- 1.7 Proper time and four-velocity -- 1.8 Mass and relativistic momentum -- Exercises 1 -- 2. Mathematical Tools -- 2.1 Multilinear algebra -- 2.2 Alternating forms -- 2.3 Manifolds -- 2.4 Tangent spaces and vector fields -- 2.5 Covariant derivatives -- 2.6 Stokesโ Theorem -- 2.7 The metric tensor -- 2.8 The covariant divergence -- 2.9 The equation d ? = ? and ?? = ? -- Exercises 2 -- 3. The Electrodynamics of Infinitesimal Charges -- 3.1 Introduction -- 3.2 The Lorentz force law -- 3.3 The electromagnetic field tensor -- 3.4 The electric and magnetic fields -- 3.5 The first Maxwell equation -- 3.6 The second Maxwell equation -- 3.7 Potentials -- 3.8 The energy-momentum tensor -- Exercises 3 -- 4. The Electrodynamics of Point Charges -- 4.1 Introduction -- 4.2 The retarded potentials and fields of a point particle -- 4.3 Radiation reaction and the Lorentz-Dirac equation -- 4.4 Calculation of the energy-momentum radiated by a point particle -- 4.5 Summary of the logical structure of electrodynamics -- Exercises 4 -- 5. Further Difficulties and Alternate Approaches -- 5.1 The Cauchy problem for the Maxwell-Lorentz system -- 5.2 Spherically symmetric solutions of the Maxwell-Lorentz system -- 5.3 Nonexistence of global solutions of the Maxwell-Lorentz system -- 5.4 An alternate fluid model -- 5.5 Peculiar solutions of the Lorentz-Dirac equation -- 5.6 Evidence for the usual energy-momentum tensor -- 5.7 Alternate energy-momentum tensors and equations of motion -- Appendix on Units -- Solutions to Exercises -- Appendix 2 -- Table of Notations