A CANONICAL APPROACH TO THE EINSTEIN–HILBERT ACTION IN TWO SPACETIME DIMENSIONS
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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 (h μν ) invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix ζ μν .
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