A CANONICAL APPROACH TO THE EINSTEIN–HILBERT ACTION IN TWO SPACETIME DIMENSIONS

Abstract

The canonical structure of the Einstein–Hilbert Lagrange density [Formula: see text] is examined in two spacetime dimensions, using the metric density [Formula: see text] and symmetric affine connection [Formula: see text] as dynamical variables. The Hamiltonian reduces to a linear combination of three first-class constraints with a local SO (2, 1) algebra. The first-class constraints are used to find a generator of gauge transformations that has a closed off-shell algebra and which leaves the Lagrangian and det (hμν) invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix ζμν.