Removing the Ostrogradski ghost from degenerate gravity theories

Abstract

The Ostrogradski ghost problem that appears in a higher-derivative system is considered for theories with constraints. A new prescription for removal of the ghost-creating momenta that come along the constrained systems is described based on the Dirac's constraint analysis. It is shown how one can make the canonical Hamiltonian bounded from below by systematically removing the constraints appearing in the system, thereby reducing the effective dimension of the phase space. To show the effect of higher-derivative terms, we consider the singularity-free Gauss-Bonnet theory coupled via a matter field to the Einstein-Hilbert action. Finally, we construct the canonical Hamiltonian for the theory that is bounded from below.