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Relativistic Electrodynamics and Differential Geometry

The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry. The intended audience is primarily mathematicians who want a bare-bones account of the fo...

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Bibliographic Details
Main Author: Parrott, Stephen
Format: eBook
Language:English
Published: New York, NY Springer New York 1987, 1987
Edition:1st ed. 1987
Subjects:
Geometry, Differential
Electrodynamics
Classical Electrodynamics
Mathematical Physics
Differential Geometry
Theoretical, Mathematical And Computational Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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 Stokes’ 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 pointparticle
  • 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

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