  We consider the problem of correlation functions in the stationary states of
one-dimensional stochastic models having conformal invariance. If one considers
the space dependence of the correlators, the novel aspect is that although one
considers systems with periodic boundary conditions, the observables are
described by boundary operators. From our experience with equilibrium problems
one would have expected bulk operators. Boundary operators have correlators
having critical exponents being half of those of bulk operators. If one studies
the space-time dependence of the two-point function, one has to consider one
boundary and one bulk operators. The Raise and Peel model has conformal
invariance as can be shown in the spin 1/2 basis of the Hamiltonian which gives
the time evolution of the system. This is an XXZ quantum chain with twisted
boundary condition and local interactions. This Hamiltonian is integrable and
the spectrum is known in the finite-size scaling limit. In the stochastic base
in which the process is defined, the Hamiltonian is not local anymore. The
mapping into an SOS model, helps to define new local operators. As a byproduct
some new properties of the SOS model are conjectured. The predictions of
conformal invariance are discussed in the new framework and compared with Monte
Carlo simulations.
