Canonical quantization of the string with dynamical geometry and anomaly free nontrivial string in two dimensions

The hamiltonian formulation of the string with a dynamical geometry and two-dimensional gravity with torsion is given. The canonical hamiltonian equals a linear combination of first-class constraints satisfying a closed algebra. It is the semidirect sum of the Virasoro algebra and the abelian subalgebra corresponding to the local Lorentz rotation. After making the canonical transformation the theory is quantized. It is proved that there exists a Fock space representation of pure two-dimensional gravity with torsion containing no central charge in the Virasoro algebra. Also constructed is a new Fock representation of the standard bosonic string. It is shown that two-dimensional string with dynamical geometry is anomaly free and describes two physical degrees of freedom. (orig.)