Electrodynamics and Special Relativity

  • Alexander Komech


The classical electrodynamics is a well established field theory, starting from formalization by Maxwell in 1855–1861 of previously known empirical facts. It serves up to now as a safe ground and a model for all subsequent field theories.

In 1862, Maxwell put forward the electromagnetic theory of light. In 1884, Heaviside recasted Maxwell’s mathematical analysis from its original form to modern vector terminology, and in the same year Poynting discovered the energy propagation in a Maxwell field. In 1886, Hertz experimentally discovered electromagnetic waves and calculated the dipole radiation. Einstein in 1905 discovered the special relativity and the covariant electrodynamics, by postulating invariance of the Maxwell equations in all inertial frames—this was justified by the Michelson and Morley crucial experiments.

The next fundamental question arises on the interaction of the Maxwell field with matter. In 1890s Lorentz introduced the electron theory of polarization and magnetization of matter; this enabled one to avoid ‘sharp questions’, reducing the problem of the matter reaction to constitutive equations.

Alternatively, one should consider all details of the interaction of charged particles with a Maxwell field. However, this question cannot be solved in the classical theory, since for a point particle, the field energy is infinite—this effect is nowadays known as the ‘ultraviolet divergence’.

To fix the situation, Abraham in 1905 introduced the model of ‘extended electron’. However, this suggestion leads to next question on the shape of electron. This question was partially clarified after the discovery of quantum mechanics (1926); however a complete answer is still a matter for the future.


Maxwell Equation Lorentz Transformation Lagrangian Density Lorentz Group Multipole Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 2.
    M. Abraham, Theorie der Elektrizität, Bd. 2: Elektromagnetische Theorie der Strahlung (Teubner, Leipzig, 1905) Google Scholar
  2. 87.
    H. Hertz, Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity Through Space (Dover, New York, 1893) Google Scholar
  3. 93.
    J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999) zbMATHGoogle Scholar
  4. 111.
    A. Komech, H. Spohn, Long-time asymptotics for the coupled Maxwell–Lorentz equations. Commun. Partial Differ. Equ. 25, 558–585 (2000) MathSciNetCrossRefGoogle Scholar
  5. 112.
    A. Komech, H. Spohn, M. Kunze, Long-time asymptotics for a classical particle interacting with a scalar wave field. Commun. Partial Differ. Equ. 22, 307–335 (1997) MathSciNetzbMATHGoogle Scholar
  6. 176.
    H. Spohn, Dynamics of Charged Particles and Their Radiation Field (Cambridge University Press, Cambridge, 2004) zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alexander Komech
    • 1
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

Personalised recommendations