Quantization of the String Inspired Dilaton Gravity and the Birkhoff Theorem

TL;DR

This paper presents a straightforward quantization scheme for the dilaton CGHS model using the Gupta-Bleuler approach, successfully reproducing classical results like the Birkhoff theorem at the quantum level.

Contribution

It introduces a linearized constraint quantization method for the dilaton CGHS model that avoids ambiguities and anomalies, ensuring classical behavior in quantum expectation values.

Findings

Quantum expectation values match classical metric and dilaton fields.

The Birkhoff theorem holds at the quantum level in this model.

No anomalies or ambiguities arise in the quantization process.

Abstract

We develop a simple scheme of quantization for the dilaton CGHS model without scalar fields, that uses the Gupta-Bleuler approach for the string fields. This is possible because the constraints can be linearized classically, due to positivity conditions that are present in the model (and not in the general string case). There is no ambiguity nor anomalies in the quantization. The expectation values of the metric and dilaton fields obey the classical requirements, thus exhibiting at the quantum level the Birkhoff theorem.