Particles on a circle in canonical lineal gravity (Q2765197)

In this article the author discusses \(1+1\)-dimensional gravity minimally coupled to \(N\)-point particles. The topology is that of a circle. A general framework is formulated for the canonical reduction of lineal gravity with compact spatial topology in the presence of a cosmological constant. This work extends previous work concerning the non-compact case. The author shows that the Hamiltonian of the system under consideration might geometrically be interpreted as the circumference functional of the circle. The canonical equations are solved for the case of pure gravity (i.e. \(N=0\)) and for \(N=1\). Setting the particle stress-energy to zero the theory reduces to the Jackiw-Teitelboim theory. A dilaton field has been included for pure gravity in \(1+1\)-dimension is known to be dynamically trivial.