  We derive an expression for the correlation function of the random force on a
soliton which is consistent with the constraints needed to integrate out the
zero modes which appear due to the broken translational symmetry of the soliton
solution. It is shown that when the constraint does not commute with the
operator which defines the correlation function, i.e. when the operator is not
physical, only low frequency phonons contributions may be considered. On the
contrary, when the correlation function of the random force on the soliton is
constructed with physical operators one may also include in a correct manner
the contributions from the optical phonons.
