Erratum: Equivalent and inequivalent canonical structures of higher order theories of gravity [Phys. Rev. D 96, 084025 (2017)]

摘要

In the manuscript, we concluded that Horowitz’s as well as Dirac’s and Ostrogradski’s formalisms fail to produce a viable quantum description of the modified Einstein-Gauss-Bonnet-dilatonic (MEGBD) action. However, later we note that such conclusion stems from an error in the solution to the classical field equations. Here, we rectify the error, along with all the expressions associated with it. In the process, we find that both Horowitz’s formalism (as well as Dirac’s and Ostrogradski’s formalisms) and modified Horowitz’s formalism produce a viable, although inequivalent, quantum description of the MEGBD action. Nevertheless, the main motivation of the manuscript, viz. “canonical formulation of higher-order theories of gravity following different prescriptions in some cases lead to equivalent and in some other cases inequivalent phase-space structures”, remains unaltered.