Canonical quantization of Polyakov's string in arbitrary dimensions

Last year Polyakov discovered the important role the trace anomaly plays in the relativistic string theory. This result means that one has to add counter terms to the string lagrangian. We give a conventional GGRT treatment of this modified lagrangian for the bosonic string. Under the boundary conditions yielding the lowest value of the classical Liouville hamiltonian, the mass spectrum starts with a tachyon. These results are semiclassical. It is shown that an exact quantization of Liouville's equation could remove the tachyon state. (orig./HSI)