2 00 1 Classical electrodynamics of point charges Massimo Marino

A simple mathematical procedure is introduced which allows redefining in a precise way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality and the relativistic covariance of the theory, and with no need for mass renormalization. The procedure provides finite expressions for the total energy-momentum of the system as well as for the lagrangian, from which the equations of motion of both particles and fields can be derived via Hamilton’s variational principle. They correspond to the Maxwell equations with point-like sources for the fields and to the relativistic Lorentz-Dirac equation for the particles, which turns out to be a second-order differential equation when the force acting on the particle is expressed in terms of the total interacting electromagnetic field. The hamiltonian formulation of the theory can be obtained in a straightforward way. This leads to an interesting comparison between the resulting divergence-free expression of the hamiltonian functional and the standard renormalization rules for perturbative quantum electrodynamics. 03.50.De, 11.10.Ef Typeset using REVTEX ∗Email address: [email protected]