Abstract

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