On energy and momentum of an ultrarelativistic unstable system

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'.