  We quantize the bosonic part of the D1 string with closed boundary conditions
on the light cone and we consider the U(1) worldsheet gauge field a dynamical
variable. We compute also 3-Reggeon vertex by the overlapping technique. We
find that the Fock space is the sum of sectors characterized by the momentum of
the U(1) Wilson line and that these sectors do not interact among them. Each
sector has exactly the same spectrum of the usual bosonic string when expressed
in properly sector dependent rescaled variables. Rescaling is forced by
factorization of the string amplitudes. We are also able to determine the
relative string coupling constant of the different sectors. It follows a
somewhat unexpected picture in which the effective action is always the same
independently on the sector but string amplitudes are only the same when
expressed in sector dependent rescaled variables.
