sl(2, R) Currents in 2D-Gravity Are Generators of Improper Gauge Transformation

The concept of improper gauge transformation, introduced originally by Regge and Teitelboim, is used to analyse the constraint structure of induced 2D-gravity, specifically in order to reveal the sl(2, R)) invariance. A local form of the induced action is taken by introducing an auxiliary scalar field. The sl(2, R)) symmetry is shown to exist in a gauge invariant way. It is shown how one can gauge fix the system to obtain the quantum sl(2, R)) currents in the light cone gauge. Interesting connections between our local formulation with geometric quantization results are mentioned briefly. Some recent canonical formulations of 2D-gravity have also been examined.