Gauge conditions in the perturbative quantization of quadratic gravity and its quantum Lagrangian

Abstract

In the perturbative formulation of the Hamiltonian of quadratic gravity, a specific gauge condition is required to hold the equivalence of the Hamiltonian equations of motion with the covariant field equations. Here we give robust evidence that this is an effect of perturbations, the exact nonperturbative equations of both formulations are equivalent, with no need of specific gauge conditions. Despite this, the required gauge condition must be imposed in the perturbative approach. We use it, together with other conditions obtained on very broad grounds, to obtain the quantum Lagrangian resulting from the integration on the canonical variables of the BFV quantization of the theory. This allow us to characterize the quantum modes from the Lagrangian perspective.