Canonical analysis of Poincare gauge theories for two-dimensional gravity

Following the general method discussed by us earlier, Liouville gravity and the two-dimensional model of non-Einsteinian gravity L approximately curv² + torsion²+cosm const can be formulated as ISO (1,1) gauge theories. In the first order formalism the models present, besides the Poincare gauge symmetry, additional local symmetries, the K-symmetries. These, related to general coordinate transformations on-shell, have canonical generators J_a satisfying a complicated constraint algebra. One can replace the J_a by means of a simple Dirac procedure, with constraints satisfying an Abelian algebra but still generating the K-symmetry. This can be done without altering the symmetry content and the equations of motion of the models. One then remarkably simplifies the canonical structure, as the constraints now satisfy only the ISO (1, 1) algebra plus an Abelian algebra. Moreover, one shows that the Poincare group can always be used consistently as a gauge group for gravitational theories in two dimensions.