Open bosonic string amplitudes

The theory of the partially $U(1)$ compactified scalar massless field on the domain on the compact Riemann surface with Nambu–Goto action is defined. The partition function is determined completely by a choice of the finite dimensional approximations. The correlation functions are the correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. The Nielsen's conjecture for the scattering amplitudes is correctly proved.