Post-Coulombian Dynamics at Order c-3

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c , then in lowest order their motion is governed by the static Coulomb Lagrangian. We investigate higher-order corrections with an explicit control on the error terms. The Darwin correction, order |v/c| ² , has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order |v/c| ³ relative to the Coulomb dynamics. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.

Authors and Affiliations

1. Zentrum Mathematik, TU München, D-80290 München, Germany e-mail: mkunze@ing-math.uni-essen.de, DE

   M. Kunze

2. Zentrum Mathematik and Physik Department, TU München, D-80290 München, Germany e-mail: spohn@mathematik.tu-muenchen.de, DE

   H. Spohn

Received February 7, 2001; accepted September 21, 2001 Online publication November 30, 2001

Reprints and permissions