A canonical formalism of f(R)-type gravity in terms of Lie derivatives

We propose a canonical formalism of f(R)-type gravity using a set of phase variables which is partly different from that used in the formalism of Buchbinder and Lyakhovich (BL). The new coordinates corresponding to the time derivatives of the metric are taken to be the Lie derivatives of the metric, which is the same as in BL. The momenta canonically conjugate to the new coordinates and Hamiltonian density are defined similarly to the formalism of Ostrogradski. It is shown that, in our formalism, the Hamiltonian is invariant under the change of the original coordinates, which is not the case in the formalism of BL