  Starting with the generators of the Poincar\'e 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
$m^{2}$ 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. Precession of polarization and transformed position operators are
among them. A deformation of the Poincar\'e algebra to the SO(4,1) deSitter one
permits the implementation of our transformation in the latter case. A
supersymmetric extension of the Poincar\'e algebra is also studied in this
context.

High Energy Physics - Theory;General Relativity and Quantum Cosmology