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It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylindercan be consistently quantized (using Dirac's approach) without imposing anyconstraints on the sign of the gravitational coupling constant or the sign (orvalue) of the cosmological constant. The quantum constraints in terms of theoriginal geometrical variables are also derived

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Dirac quantization of two-dimensional dilation gravity minimally coupled to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>massless scalar fields

Dirac quantization of two-dimensional dilation gravity minimally coupled toNmassless scalar fields