Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model

TL;DR

This paper introduces a new canonical formulation for 2D dilatonic models using polar variables, transforming the constraint algebra into a Lie algebra, and constructs observables and a reduced Hamiltonian suitable for loop quantum gravity quantization.

Contribution

It develops a novel set of variables and transformations that simplify the constraint algebra of 2D dilatonic models, enabling their quantization via loop methods.

Findings

Constraint algebra becomes a Lie algebra after transformations

Dirac observables and a reduced Hamiltonian are explicitly constructed

Formulation applicable to models with matter, facilitating loop quantization

Abstract

We consider a class of two dimensional dilatonic models, and revisit them from the perspective of a new set of "polar type" variables. These are motivated by recently defined variables within the spherically symmetric sector of 4D general relativity. We show that for a large class of dilatonic models, including the case \emph{with} matter, one can perform a series of canonical transformations in such a way that the Poisson algebra of the constraints becomes a Lie algebra. Furthermore, we construct Dirac observables and a reduced Hamiltonian that accounts for the time evolution of the system. Thus, with our formulation, the systems under consideration are amenable to be quantized with loop quantization methods.