Propagation of particles and strings in one-dimensional Universe

We review the basics of the dynamics of closed strings moving along the discretized line \Z. The string excitations are described by a field \phi_x(\tau) where x is the position of the string in the embedding space and \tau is a semi-infinite ``euclidean time'' parameter related to the longitudinal mode of the string. Interactions due to splitting and joining of closed strings are taken into account by a local potential and occur only along the edge \tau =0 of the semi-plane (x, \tau).