Canonical Analysis of Poincare' Gauge Theories for Two Dimansional Gravity

Abstract

Following the general method discussed in Refs.[1,2], Liouville gravity and the 2 dimensional model of non-Einstenian gravity $\mathcal{L}\sim cur{v}^2+torsio{n}^2+cosm.const.$ can be formulated as ISO(1,1) gauge theories. In the first order formalism the models present, besides the Poincaré gauge symmetry, additional local symmetries. We show that in both models one can fix these additional symmetries preserving the ISO(1,1) gauge symmetry and the diffeomorphism invariance, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the ISO(1,1) algebra. After the additional symmetry is fixed, the equations of motion are unaltered. One thus remarkably simplifies the canonical structure, especially of the second model. Moreover, one shows that the Poincaré group can always be used consistently as a gauge group for gravitational theories in two dimensions.

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References in corpus (3)

• Poincaré Gauge Theory for Gravitational Forces in (1+1) Dimensions
• Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions
• All Symmetries of Non-Einsteinian Gravity in $d=2$

Cited by in corpus (1)

• Reply to `Comment on Gravity and the Poincare' Group'