Canonical doubly special relativity theory

For a certain example of a ``doubly special relativity theory'' the modified space-time Lorentz transformations are obtained from the momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time metric is constructed, which is essentially invariant under the modified Lorentz transformations. By associating such a metric to every Planck cell in space and to the energy-momentum contained in it, a solution of the problem of macroscopic bodies in doubly special relativity is suggested.