By explicitly including a representative for T, as well as one for P, a representation of the full Lorentz group O(3; 1) is obtained. A subtle problem appears however in application to physics, in particular quantum mechanics. When considering the full Poincaré group, four more generators, the P, in addition to the J and K generate the group. These are interpreted as generators of translations. The time-component P is the Hamiltonian H. The operator T satisfies the relation