Appendix: Ray class characters of bounded order and bounded conductor

Appendix to: A. Karnataki, Self-dual Artin representations of dimension three. Journal of Number Theory, v. 173, pp. 442 - 446. https://doi.org/10.1016/j.jnt.2016.09.00

Quaternionic Artin representations of Q

Isomorphism classes of dihedral Artin representations of ℚ can be counted asymptotically using Siegel's asymptotic averages of class numbers of binary quadratic forms. Here we consider the analogous problem for quaternionic representations. While an asymptotic formula is out of our reach in this case, we show that the asymptotic behaviour in the two cases is quite different

Rutherford scattering with radiation damping

We study the effect of radiation damping on the classical scattering of charged particles. Using a perturbation method based on the Runge-Lenz vector, we calculate radiative corrections to the Rutherford cross section, and the corresponding energy and angular momentum losses.Comment: Latex, 11 pages, 4 eps figure

The dynamics of a charged particle

Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can classically not be a point particle because of the Coulomb field divergence, my derivation accounts for that by imposing a basic condition on the external force. That condition ensures that the particle's finite size charge distribution looks like a point charge to the external force. Finite radius charge distributions are known not to lead to differential equations of motion. The present work is in agreemnent with the results by Spohn and by others. An example, uniform acceleration, demonstrates what the above basic condition entails. For clarity of the argument, I discuss the non-relativistic case before the relativistic one.Comment: 11 page