New canonical analysis for higher order topologically massive gravity

Abstract

A detailed Gitman–Lyakhovich–Tyutin analysis for higher-order topologically massive gravity is performed. The full structure of the constraints, the counting of physical degrees of freedom, and the Dirac algebra among the constraints are reported. Moreover, our analysis presents a new structure into the constraints and we compare our results with those reported in the literature where a standard Ostrogradski framework was developed.

Canonical analysis for Chern-Simons modification of general relativity

“…Hence, after a long algebraic work, we find that the matrix W IJ has 12 null vectors, therefore, this implies that will there 12 first class constraints [19]. The first class constraints are given given by…”

“…We can observe that the action is a higher order theory and we will use the GLT method for performing the canonical analysis. By following the GLT framework, we introduce the following change of variables [18,19]…”

“…On the other hand, the GLT framework is a generalization of Ostrogradski's method, it is based on the introduction of extra fields reducing a problem with higher temporal derivatives to one with first-order time derivatives. Then by using either the definition of the momenta for all the fields or the introduction of the Dirac brackets, the second class constraints, and non-physical degrees of freedom (extra fields) can be removed [18,19]. In this manner, in this paper, we will use the GLT formalism for performing our analysis due to its consistency and the fact that allows us to know the complete structure of the constraints.…”

The Hamilton–Jacobi analysis for higher-order Chern–Simons gravity

“…However, the identification of the constraints is not easy to develop; in some cases, the constraints are fixed by hand in order to obtain a consistent algebra [33] and this yields the opportunity to work with alternative methods. On the other hand, the GLT framework is based on the introduction of extra variables which transforms a problem with higher time derivatives to one with only first-order ones then, by using the Dirac brackets the second class constraints and the extra variables can be removed [34].…”