HIGHER-ORDER ACTION FOR THE INTERACTION OF THE STRING WITH THE DILATON

A new theory for the string interacting with a dilaton background fiel d is analyzed. In the action considered, the metric in the world-sheet of the string is the induced metric, and the theory presents second o rder time derivatives. The canonical formalism is developed and it is shown that first and second class constraints appear. The degrees of f reedom are the same as for the free bosonic string. The light cone gau ge is used to reduce to the physical modes and to compute the physical Hamiltonian.