Quantized string models

We discuss and compare the Lorentz covariant path integral quantization of the three bose string models, namely, the Nambu, Eguchi and Brink-Di Vecchia-Howe-Polyakov (BDHP) ones. Along with a critical review of the subject with some uncertainties and ambiguities clearly stated, various new results are presented. We work out the form of the BDHP string ansatz for the Wilson average and prove a formal inequivalence of the exact Nambu and BDHP models for any space-time dimension d. The above three models, known to be equivalent on the classical level, are shown to be equivalent in a semiclassical approximation near a minimal surface and also in the leading $\text{1}\text{d}\text{-}\text{approximation}$ for the static $\text{q}$q-potential. We analyse scattering amplitudes predicted by the BDHP string and find that when exactly calculated for d < 26 they are different from the old dual ones, and possess a non-linear spectrum which may be considered as free from tachyons in the ground state.