Algebraic analysis of a model of two-dimensional gravity

TL;DR

This paper performs an algebraic analysis of a two-dimensional gravity model's Hamiltonian formulation, revealing a key algebraic structure and providing explicit eigenvectors of the canonical Hamiltonian.

Contribution

It identifies the Poisson brackets algebra of secondary constraints with the SO(2,1)-algebra and explicitly derives eigenvectors of the canonical Hamiltonian.

Findings

Poisson brackets algebra matches SO(2,1)-algebra

Eigenvectors of the canonical Hamiltonian are explicitly obtained

Provides a closed-form expression for eigenvectors

Abstract

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.