  Motivated by recent works on the origin of inertial mass, we revisit the
relationship between the mass of charged particles and zero-point
electromagnetic fields. To this end we first introduce a simple model
comprising a scalar field coupled to stochastic or thermal electromagnetic
fields. Then we check if it is possible to start from a zero bare mass in the
renormalization process and express the finite physical mass in terms of a
cut-off. In scalar QED this is indeed possible, except for the problem that all
conceivable cut-offs correspond to very large masses. For spin-1/2 particles
(QED with fermions) the relation between bare mass and renormalized mass is
compatible with the observed electron mass and with a finite cut-off, but only
if the bare mass is not zero; for any value of the cut-off the radiative
correction is very small.
