  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.
