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 Tmu nu is integrated over a hyperplane orthogonal to the velocity Vlambda of the observer. The resulting energy tensor Tmu 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 Tmu 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.