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A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions

N. Kiriushcheva·S. V. Kuzmin·D. G. C. McKeon
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Abstract

The canonical structure of the Einstein-Hilbert Lagrange density $L=\sqrt{-g}R$ is examined in two spacetime dimensions, using the metric density $h^{μν}\equiv \sqrt{-g}g^{μν}$ and symmetric affine connection $Γ_{σβ}^λ$ 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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N. Kiriushcheva, S. V. Kuzmin, D. G. C. McKeon. 2005-03-12. A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions. https://doi.org/10.1142/s0217732305018086

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