We consider the model suggested by Wang and Unruh [Phys. Rev. D 89, 085009 (2014)] for the 1+1-dimensional mirror moving in the quantum vacuum. We consider the relation of this model to the problem of the polaron—the electron moving in the vacuum of the quantum field of phonons. We introduce the field-theoretical model of such a mirror. It contains the multicomponent spinor field interacting with the scalar field. We discuss the source of the logarithmic divergence in the mirror mass and its relation to the problem of the divergencies in vacuum energy.