Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse

TL;DR

This paper develops an anomaly-free Dirac constraint quantization for a 2D dilatonic gravity model inspired by string theory, preserving classical degrees of freedom and providing a linear quantum dynamics framework.

Contribution

It introduces a novel quantization approach for the CGHS model that maintains classical degrees of freedom and yields linear equations of motion at the quantum level.

Findings

Quantum theory retains all classical degrees of freedom.

Heisenberg equations of motion are linear and match classical form.

Quantization induces the physical geometry from canonical variables.

Abstract

We present an anomaly-free Dirac constraint quantization of the string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional spacetime. We show that the quantum theory has the same degrees of freedom as the classical theory; namely, all the modes of the scalar field on an auxiliary flat background, supplemented by a single additional variable corresponding to the primordial component of the black hole mass. The functional Heisenberg equations of motion for these dynamical variables and their canonical conjugates are linear, and they have exactly the same form as the corresponding classical equations. A canonical transformation brings us back to the physical geometry and induces its quantization.