We address to the Poynting theorem for the bound electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \ and bound electric field \ are generated by the same source (...) charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way, we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor. (shrink)

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, (...) we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined. (shrink)