Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity

TL;DR

This paper develops a geometrodynamical formulation for two-dimensional dilaton gravity, enabling a canonical and quantum analysis that preserves key classical properties like Birkhoff's theorem.

Contribution

It introduces new field variables related to spacetime geometry, allowing quantization of the model using established techniques from black hole physics.

Findings

Model can be quantized using geometrodynamical variables.

Quantum Birkhoff theorem is established.

Framework applies to arbitrary dilatonic potentials.

Abstract

Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential can be discussed in a unitary way, both in the Lagrangian and canonical frameworks, by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize the well-known geometrodynamical variables used in the discussion of the Schwarzschild black hole. So the model can be quantized using the techniques developed for the latter case. The resulting quantum theory exhibits the Birkhoff theorem at the quantum level.