Classical electrodynamics and the definition of an energy tensor for a system of charged particles and electromagnetic fields

Using an invariant spatial volume element the energy-density tensor T mu nu is integrated over a hyperplane orthogonal to the velocity V lambda of the observer. The resulting energy tensor T mu nu for the system yields the momentum and energy of the system relative to a given observer in the usual way. It is shown that the usual conservation theorems for the momentum of a free field and the momentum radiated by an accelerated particle are recovered, but the expression obtained for the (bound) velocity-field momentum differs from the usual expression of this quantity given in the literature. The new definition of momentum results in a rational definition when applied to two or more particles, which is in contradistinction to the usual definition which cannot be generalised for two or more particles unambiguously. The definition of T mu nu given here is the flat space-time specialisation of a definition previously given by the author in the context of general relativity. Thus a uniform prescription for the treatment of problems concerning energy and momentum is achieved together with the resolution of a long-standing conceptual problem.