Zweibein Operator Formalism of Two-Dimensional Quantum Gravity

The unitary, manifestly covariant operator formalism of two-dimensional quantum gravity, presented previously, is extended to the zweibein formalism. All the two-dimensional (anti) commutation relations between primary fields are obtained in closed form. The four degrees of freedom of the zweibein are shown to be realized as q-number transformation functions of the general coordinate transformation, the local Lorentz transformation and the Weyl transformation. As the result, the explicit expression for the gravitgational extension of the Pauli-Jordan D-function is found in terms of the zweibein. Bosonized operator solutions known in solvable two-dimensional models are extended to the quantum-gravity case through the above q-number transformations