Perusing Buchbinder--Lyakhovich canonical formalism for Higher-Order Theories of Gravity

TL;DR

This paper compares different Hamiltonian formalisms for higher-order gravity theories, demonstrating that Buchbinder--Lyakhovich's approach can be made consistent by suitable modifications, aligning it with Horowitz's and Dirac's methods.

Contribution

It shows that the Buchbinder--Lyakhovich formalism, previously thought to have issues, can be rendered consistent for higher-order gravity theories through specific modifications.

Findings

Pathologies in BL formalism are removable with proper action reformulation.

All formalisms yield consistent phase-space structures after addressing total derivatives.

The modified BL approach is simpler and effective for higher-order gravity theories.

Abstract

Ostrogradsky's, Dirac's and Horowitz's techniques of higher order theories of gravity produce identical phase-space structures. The problem is manifested in the case of Gauss-Bonnet-dilatonic coupled action in the presence of higher-order term, in which case, classical correspondence can't be established. Here, we explore yet another technique developed by Buchbinder and his collaborators (BL) long back and show that it also suffers from the same disease. However, 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.