Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity

TL;DR

This paper investigates the covariant phase space and conservation laws in 2D dilaton gravity, focusing on symplectic structure, asymptotic symmetries, and the role of Noether charges in the canonical formalism.

Contribution

It provides an explicit computation of the symplectic structure and clarifies how finiteness conditions constrain asymptotic symmetries in 2D dilaton gravity.

Findings

Explicit symplectic structure and potential derived.

Asymptotic symmetries restricted by finiteness conditions.

On-shell Lagrangian vanishes, enabling covariant potential for symplectic current.

Abstract

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.