Bambusi-D., Noja-D.
ON CLASSICAL ELECTRODYNAMICS OF POINT PARTICLES
AND MASS RENORMALIZATION
(88K, TeX)
ABSTRACT. We consider the problem of finding rigorous results for
the dynamics of a classical charged point particle interacting with the
electromagnetic field, as described by the standard Maxwell--Lorentz
equations. Some results are given for the corresponding linearized
system, i.e. the so called dipole approximation, in the presence of a
mechanical linear restoring force. We regularize the system by taking a
form factor for the particle (Pauli--Fierz model) and
study the limit of the particle's motion as the regularization is
removed. We prove that (i) if the regularization is removed but mass is
not
renormalized the motion is trivial (i.e. the particle does
not move at all); (ii) if the regularization is removed and mass is
renormalized, the particle's motion corresponding to smooth initial data
for the field has a well defined nontrivial limit; (iii) in the case of
vanishing initial field the limit motion satisfies exactly the
Abraham--Lorentz--Dirac
equation; (iv) for generic initial data the limit motion is runaway.