On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions

TL;DR

This paper demonstrates that the Einstein-Hilbert action in two dimensions can be formulated Hamiltonianly without modifications, revealing constraints and gauge transformations while preserving general covariance.

Contribution

It shows that the 2D Einstein-Hilbert action is not necessarily a total divergence and provides a Hamiltonian formulation with explicit constraints and gauge transformations.

Findings

Hamiltonian formulation of 2D Einstein-Hilbert action is possible without modifications.

Constraints and gauge transformations of the metric tensor are explicitly derived.

The triviality of Einstein equations in 2D does not imply the action is a total divergence.

Abstract

It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a coordinate system is not fixed. Consequently, a Hamiltonian formulation is possible without any modification of the two dimensional Einstein-Hilbert action. We find the resulting constraints and the corresponding gauge transfromations of the metric tensor.