  The two dimensional analog of the Hadamard state condition is used to specify
the local Hadamard states associated with a linear quantum field coupled to a
two dimensional gravitational background. To characterize a local Hadamard
state corresponding to a physical vacuum state, we apply a superselection rule
in which the state dependent part of the two-point function is determined in
terms of a dynamical scalar field. It implies a basic connection between the
vacuum state and a scalar field coupled to gravity. We study the
characteristics of the Hadamard vacuum state through this superselection rule
using two different background metrics, the two dimensional analog of the
schwarzschild and FRW metric.
