Two-dimensional metric and tetrad gravities as constrained second order systems

TL;DR

This paper develops a Hamiltonian formulation for two-dimensional metric and tetrad gravities using a generalized Ostrogradsky method, analyzing their constraint algebra and gauge symmetries.

Contribution

It introduces a Hamiltonian approach for 2D gravities as constrained higher-derivative systems, extending previous methods to this context.

Findings

Derived the Poisson bracket structure of constraints.

Analyzed gauge transformations in 2D gravities.

Provided a framework for quantization of 2D gravity models.

Abstract

Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as constrained higher-derivative theories. The algebraic structure of the Poisson brackets of the constraints and the corresponding gauge transformations are investigated in both cases.