Perusing Buchbinder–Lyakhovich Canonical Formalism for Higher-Order Theories of Gravity

Abstract

Ostrogradsky’s, Dirac’s, and Horowitz’s techniques in terms of higher-order theories of gravity produce identical phase-space structures. The problem with these techniques is manifested in the case of Gauss–Bonnet–dilatonic coupled action in the presence of higher-order term, in which case, classical correspondence cannot be established. Here, we explore another technique developed by Buchbinder and their collaborators (BL) and show that it also suffers from the same disease. However, when expressing the action in terms of the three-space curvature, and removing ‘the total derivative terms’, if Horowitz’s formalism or even Dirac’s constraint analysis is pursued, all pathologies disappear. Here, we show that the same is true for BL formalism, which appears to be the simplest of all the techniques to handle.