  We study an electron bunch together with its self-fields from the viewpoint
of basic dynamical quantities. This leads to a methodological discussion about
the definition of energy and momentum for fully electromagnetic systems and
about the relation between covariance of the energy-momentum pair and
stability. We show here that, in the case of unstable systems, there is no mean
to define, in a physically meaningful way, a total energy-momentum four-vector:
covariance of the energy-momentum pair follows from the stability of the system
and viceversa, as originally pointed out by Henry Poincare'.
