A canonical formalism for a higher-curvature 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.