  We present full expressions for the surface part of polarization tensor of a
Dirac fermion confined in a half-space in $3+1$ dimensions. We compare this
tensor to the polarization tensor of eventual surface mode (which is a $2+1$
dimensional Dirac fermion) and find essential differences in the conductivities
in both Hall and normal sectors. Thus, the interaction with electromagnetic
field near the boundary differs significantly in the full model and in the
effective theory for the surface mode.
