The canonical structure of the Einstein-Hilbert Lagrange density $L=\sqrt{ -g}R$ is examined in two spacetime dimensions, using the metric density $h^{ \mu \nu}\equiv \sqrt{ -g}g^{ \mu \nu}$ and symmetric affine connection $\Gamma_{ \sigma \beta}^\lambda $ 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 $\det (h^{ \mu \nu})$ invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix $\zeta_{ \mu \nu}$.
Categories: hep-th