CANONICAL-ANALYSIS OF POINCARE GAUGE-THEORIES FOR 2-DIMENSIONAL GRAVITY

Following the general method discussed by us earlier, Liouville gravit y and the two-dimensional model of non-Einsteinian gravity L approxima tely curv2 + torsion2 + cosm const can be formulated as ISO(1,1) gauge theories. In the first order formalism the models present, besides th e Poincare gauge symmetry, additional local symmetries, the kappa-symm etries. These, related to general coordinate transformations on-shell, have canonical generators J(a) satisfying a complicated constraint al gebra. One can replace the J(a). by means of a simple Dirac procedure, with constraints satisfying an Abelian algebra but still generating t he kappa-symmetry. This can be done without altering the symmetry cont ent and the equations of motion of the models. One then remarkably sim plifies the canonical structure, as the constraints now satisfy only t he ISO(1,1) algebra plus an Abelian algebra. Moreover, one shows that the Poincare group can always be used consistently as a gauge group fo r gravitational theories in two dimensions.