On the Canonical Formalism for a Higher-Curvature Gravity

TL;DR

This paper develops a canonical formalism for higher-curvature gravity theories with Lagrangians depending on a function of scalar curvature, enabling Hamiltonian analysis of such theories.

Contribution

It introduces a Hamiltonian formulation for f(R) gravity using a canonical transformation, extending the formalism to higher-derivative gravitational actions.

Findings

Derived the local Hamiltonian for f(R) gravity

Established a canonical transformation method for higher-derivative theories

Provided a framework for Hamiltonian analysis of modified gravity

Abstract

Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal L}=\sqrt{-\det g_{\mu\nu}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.