Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-01-26
Mod.Phys.Lett. A20 (2005) 1895-1902
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, references are added and the compact form of gauge transformations is given
Scientific paper
10.1142/S0217732305018086
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 $\zeta_{\mu \nu}$.
Kiriushcheva N.
Kuz'min S. V.
McKeon Dennis G. C.
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