Canonical Analysis of Poincare' Gauge Theories for Two Dimansional Gravity

TL;DR

This paper performs a canonical analysis of two-dimensional Poincaré gauge theories, demonstrating how to fix extra symmetries to simplify the constraint algebra while preserving gauge and diffeomorphism invariance.

Contribution

It shows that additional local symmetries in 2D Poincaré gauge theories can be fixed without altering equations of motion, simplifying the canonical structure.

Findings

Constraints satisfy the ISO(1,1) algebra after fixing symmetries

The gauge group ISO(1,1) can be consistently used in 2D gravity

Simplification of the canonical structure in Liouville and non-Einsteinian models

Abstract

Following the general method discussed in Refs.[1,2], Liouville gravity and the 2 dimensional model of non-Einstenian gravity ${\cal L} \sim curv^2 + torsion^2 + cosm. const.$ can be formulated as ISO(1,1) gauge theories. In the first order formalism the models present, besides the Poincar\'e 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 Poincar\'e group can always be used consistently as a gauge group for gravitational theories in two dimensions.