On the canonical formalism of $f(R)$-type gravity using Lie derivatives

Understand

We present a canonical formalism of the $f(R)$-type gravity using the Lie derivatives instead of the time derivatives by refining the formalism of our group.

• The previous formalism is a direct generalization of the Ostrogradski's formalism.
• However the use of the Lie derivatives was not sufficient in that Lie derivatives and time derivatives are used in a mixed way, so that the expressions are somewhat complicated.
• In this paper, we use the Lie derivatives and foliation structure of the spacetime thoroughly, which makes the procedure and the expressions far more concise.