Nonlinear transforms of momenta and Planck scale limit

Starting with the generators of the Poincare group for arbitrary mass (m) and spin (s), a nonunitary transformation is implemented to obtain momenta with an absolute Planck scale limit. In the rest frame (for m>0) the transformed energy coincides with the standard one, both being m. As the latter tends to infinity under Lorentz transformations the former tends to a finite upper limit m coth(lm)=l-1+O(l), where l is the Planck length and the mass-dependent nonleading terms vanish exactly for zero rest mass. The invariant m2 is conserved for the transformed momenta. The speed of light continues to be the absolute scale for velocities. We study various aspects of the kinematics in which two absolute scales have been introduced in this specific fashion. The precession of polarization and transformed position operators are among them. A deformation of the Poincare algebra to the SO(4,1) de Sitter one permits the implementation of our transformation in the latter case. A supersymmetric extension of the Poincare algebra is also studied in this context