1207.1745 (Charles Nakhleh)

The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of
modern renormalization theory    [PDF]

Charles Nakhleh

In this pedagogical note, I revisit the problem of the equation of motion of a relativistic classical electron coupled to the electromagnetic field, a problem that is not so much addressed in the education of the typical physics student as put aside en route to the more difficult problems that arise in quantum field theory. The equations governing the motion of a classical electron under the influence of its electromagnetic field have been discussed for a century, and continue to be actively investigated in the current literature, but it appears that a consistent approach to the problem from the point of view of modern renormalization theory has not previously been reported. I show that the methods of modern renormalization theory applied to the full Maxwell-Lorentz system provide a natural and intuitive derivation of the Lorentz-Dirac equation as an effective description of the electron motion valid for distances large compared to the classical electron radius. Moreover, a consistent treatment of the Lorentz-Dirac equation as an effective theory leads directly to the Landau-Lifshitz equation and provides a clear conceptual basis for Rohrlich's recent approach to that equation (Phys. Rev. {\bf E77}, 046609 (2008)). A full and careful computation of the self-field of the classical electron is given to provide the student a nontrivial problem in renormalization that does not require mastering the apparatus of quantum field theory.

View original: http://arxiv.org/abs/1207.1745