D. Louismartinez, DIRAC QUANTIZATION OF 2-DIMENSIONAL DILATION GRAVITY MINIMALLY COUPLED TO N MASSLESS SCALAR FIELDS, Physical review. D. Particles and fields, 55(12), 1997, pp. 7982-7984
It is shown that the Callan-Giddings-Harvey-Strominger theory on S(1)x
R can he consistently quantized (using Dirac's approach) without impos
ing any constraints on the sign of the gravitational coupling constant
or the sign (or value) of the cosmological constant. The quantum cons
traints in terms of the original geometrical variables ax also derived
.