Lorentz covariance of the mass-polariton theory of light

In the mass-polariton (MP) theory of light formulated by us recently [Phys. Rev. A 95, 063850 (2017)], light in a medium is described as a coupled state of the field and matter. The key result of the MP theory is that the optical force of light propagating in a transparent material drives forward an atomic mass density wave (MDW). In previous theories, it has been well understood that the medium carries part of the momentum of light. The MP theory is fundamentally different since it shows that this momentum is associated with the MDW that carries a substantial atomic mass density and the related rest energy with light. In this work, we prove the Lorentz covariance of the MP theory and show how the stress-energy-momentum (SEM) tensor of the MP transforms between arbitrary inertial frames. We also compare the MP SEM tensor with the conventional Minkowski SEM tensor and show how the well-known fundamental problems of the Minkowski SEM tensor become solved by the SEM tensor based on the MP theory. We have particularly written our work for non-expert readers by pointing out how the Lorentz transformation and various conservation laws and symmetries of the special theory of relativity are fulfilled in the MP theory.