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

Abstract

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.

arXiv comment11 pages, no figures, Version accepted for publication in Eur. Phys. J. Plus

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• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Extended Chern-Simons model for a vector multiplet