NUMERICAL-STUDIES ON CLASSICAL ELECTRODYNAMICS

We report on some numerical results in classical electrodynamics, described as a Hamiltonian system; we consider the standard Pauli-Fierz model, in which the field obeys Maxwell's equations with current due to a charged particle, while the particle satisfies Newton's equation with the Lorentz force. At variance with the standard treatments where the particle motion is computed by neglecting the electromagnetic field, here neither the motion of the particle, nor the field are given in advance. The main result concerns the spectrum of the radiation emitted during a scattering of the particle: we show that there exists a frequency threshold such that only the modes with lower frequency absorb energy, while the other ones seem to remain somehow attached to the particle, so that they just contribute to the electromagnetic mass of the particle. Furthermore we illustrate an idea stated by Einstein in his famous paper of the year 1909, where he suggests that the irreversibility of the electromagnetic emission is a statistical phenomenon.