Quantization of the string inspired dilaton gravity and the Birkhoff theorem

We show that, for the pure dilaton CGHS model, the Gupta-Bleuler quantization is viable because the constraints can be linearized due to positivity conditions 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.