Perturbative quantum gravity coupled to particles in (1+1) dimensions

We consider the problem of (1+1)- dimensional quantum gravity coupled to particles. Working with the canonically reduced Hamiltonian, we obtain its post-Newtonian expansion for two identical particles. We quantize the ( 1+1)dimensional Newtonian system first, after which explicit energy corrections to second order in c(-1) are obtained. We compute the perturbed wavefunctions and show that the particles are bound less tightly together than in the Newtonian case.