Canonical Analysis of the Jackiw-Teitelboim Model in the Temporal Gauge. I. The Classical Theory

TL;DR

This paper analyzes the classical canonical structure of the Jackiw-Teitelboim 2D gravity model in the temporal gauge, focusing on constraints, gauge fixing, and Dirac observables to prepare for quantization.

Contribution

It provides a detailed canonical analysis, including gauge fixing and Dirac brackets, of the Jackiw-Teitelboim model, which is essential for its loop quantum gravity quantization.

Findings

Derived the Dirac bracket algebra for the model.

Identified and calculated Dirac observables.

Clarified the structure of constraints in the classical theory.

Abstract

As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial gauge fixing of the temporal type being performed, the resulting second class constraints are sorted out and the corresponding Dirac bracket algebra is worked out. Dirac observables of this classical theory are then calculated.