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We quantize the bosonic part of the D1 string with closed boundary conditionson the light cone and we consider the U(1) worldsheet gauge field a dynamicalvariable. We compute also 3-Reggeon vertex by the overlapping technique. Wefind that the Fock space is the sum of sectors characterized by the momentum ofthe U(1) Wilson line and that these sectors do not interact among them. Eachsector has exactly the same spectrum of the usual bosonic string when expressedin properly sector dependent rescaled variables. Rescaling is forced byfactorization of the string amplitudes. We are also able to determine therelative string coupling constant of the different sectors. It follows asomewhat unexpected picture in which the effective action is always the sameindependently on the sector but string amplitudes are only the same whenexpressed in sector dependent rescaled variables.

Light cone quantization and interactions of a new closed bosonic string inspired to D1 string