Abstract
The theory of a string (with fermion degrees of freedom) that evolves in a curved space-time (in the space of a Lie group) is considered. The aim behind this investigation is to investigate the construction of the vertex operators and the corresponding dual scattering amplitudes of the new strings. The method of constructing functionals (corresponding to the vertex operators) that commute with the constraints is based on the fact that the entire treatment is given in an arbitrary gauge, when the Lagrangian multipliers that arise in the Hamiltonian approach are not fixed but regarded at all stages as arbitrary functions. All the main results are obtained in superfield language, which arises in our approach as a result of the compact expression of the Hamilton equations of motion.
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