Proof that the formulations of the electrodynamics of moving bodies are equivalent

The existing formulations of electrodynamics in matter have different expressions for the 4-force acting on the matter and energy-momentum tensors in the electromagnetic field. In this paper, the formulations by Minkowski, Ampère, Boffi and Chu are examined and shown to be equivalent. It is shown that all these formulations can be written as the equations of balance of momentum, energy and angular momentum in the form $\partial_\beta T^{\alpha\beta}=0$, $T^{\alpha\beta}=T^{\beta\alpha}$. The differences in the formulations are due merely to different definitions for the mechanical part of the energy-momentum tensor $T^{\alpha\beta}$.