Hamiltonian Approach to 2+1 Dimensional Gravity

It is shown that the reduced particle dynamics of 2 + 1 dimensional gravity in the maximally slicing gauge is of hamiltonian nature. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser, Jackiw, ’t Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the Hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle Hamiltonian is given and the Green function computed.