  We have used a two-dimensional analog of the Hadamard state-condition to
study the local constraints on the two-point function of a linear quantum field
conformally coupled to a two-dimensional gravitational background. We develop a
dynamical model in which the determination of the state of the quantum field is
essentially related to the determination of a conformal frame. A particular
conformal frame is then introduced in which a two-dimensional gravitational
equation is established.
