[en] It is shown that the usual cut-off procedure (α cut-off parameter) employed in the boson representation of the fermion field opepators of the one-djmensional two-fermion model (TFM) is an incorrect one as the computator of the hermitean-conjugate field operators at the same space-point fails to fulfil a certain relationship which was pointed out long ago by Jordan. The complete form of the boson representation (including the zero-mode) of a single fermion field and the correct values of the cut-off parameter α is reviewed following Jordan and generalized to the TFM. The cut-off parameter α corresponds to a bandwidth cut-off and Jordan's boson representation is exact only in the limit α → 0. The additional zero-mode terms make the exact solution of the backscattering and umklapp scattering problem to be valid only if a supplementary condition is imposed on the coupling constants. Using the present bosonization technique all the inconsistencies of the TFM are removed. The one-particle Green's function and response functions of the Tomonaga-Luttinger model (TLM) are calculated and found to be identical with those obtained by direct diagram summation. The energy gap appearing in the spectrum of the TFM with backscattering and umklapp scattering for certain values of the coupling constants is shown to be proportional to the momentum transfer cut-off γ^-1 which has to be kept finite while α goes to zero. Under such conditions the anticommunication relations and Jordan's commutator are invariant under the canonical transformation on the boson operators that diagonalizes the Hamiltonian of the TLM. The charge-density response function of the TFM with backscattering is perturbationally calculated up to the first order. The cut-off α^-1 applies in the same way to terms which differ only by their spin indices in the expression of this response function. The charge-density response function is also evaluated at low frequencies for the exactly soluble TFM with backscattering by using Jordan's cut-off procedure. (author)