Refined form of the paper "Canonical formalism of the f(R)-type gravity in terms of Lie derivatives"

Abstract

We refine the presentation of the previous paper of our group, Y.Ezawa et al., Class. Quantum Grav. {\bf 23} (2006), 3205 [arXiv:gr-qc/0507060]. In that paper, we proposed a canonical formalism of f(R)-type generalized gravity by using the Lie derivatives instead of the time derivatives. However, the use of the Lie derivatives was not sufficient. In this note, we make use of the Lie derivatives as far as possible, so that no time derivatives are used.