On a Two-Dimensional Symplectic Space-Time

We realize the hamiltonian action of the one spatial Poincare group G, analogous to the projective unitary representation, on a coadjoint orbit of G whic we interpret as a symplectic space-time where the time is associated to a physical quantity of cohomological origine (the force f). This time is the time delay necessary tor the system under the force f to have momentum p.