Particles on a Circle in Canonical Lineal Gravity

A description of the canonical formulation of lineal gravity minimally coupled to N point particles in a circular topology is given. The Hamiltonian is found to be equal to the time-rate of change of the extrinsic curvature multiplied by the proper circumference of the circle. Exact solutions for pure gravity and for gravity coupled to a single particle are obtained. The presence of a single particle significantly modifies the spacetime evolution by either slowing down or reversing the cosmological expansion of the circle, depending upon the choice of parameters.