  We consider the model suggested by Wang and Unruh \cite{WangUnruh2013} for
the $1+1$ D mirror moving in the quantum vacuum. We consider the relation of
this model to the problem of 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 multi - component 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.
