Path integral quantization of 2D-gravity (Q1878347)

In the present work the author investigates the 2D gravity by using the Hamilton-Jacobi method. The equations of motion and the action function are obtained as total differential equations in many variables. The integrability condition leeds to obtain the new integrable set of equations of motion and the action function. Hence, the canonical path integral can be obtained directly as an integration over the canonical phase-space coordinates without any need to introduce any extra non-physical variables.