General relativity in two dimensions: A Hamilton–Jacobi analysis

We analyzed the constraint structure of the Einstein–Hilbert first-order action in two dimensions using the Hamilton–Jacobi approach. We were able to find a set of involutive, as well as a set of non-involutive constraints. Using generalized brackets we showed how to assure integrability of the theory, to eliminate the set of non-involutive constraints and how to build the field equations.