Tensor Lorentz Force Representation Yields a New Electromagnetic Canonical Energy-Momentum Tensor

As is known, the Maxwell stress-energy tensor typically used in electromagnetism is not a canonical tensor in the sense of Noether, since its four-divergence is not zero in the presence of sources, in other words, outside of free space. Indeed, the result provided by the calculation of the four-divergence of this tensor is the opposite of the four-vector generalizing the Lorentz force density. The idea is to associate with it a tensor constructed from potentials and sources, such that its four-divergence is the opposite of that of the Maxwell tensor. The distribution of sources will also be analyzed in light of fluid mechanics, allowing us to account for its influence in terms of generated pressure.