  Based on a linear realization formulation of a quantum relativity -- the
proposed relativity for quantum `space-time', we introduce the
Poincar\'e-Snyder relativity and Snyder relativity as relativities in between
the latter and the well known Galilean and Einstein cases. We discuss how the
Poincar\'e-Snyder relativity may provide a stronger framework for the
description of the usual (Einstein) relativistic quantum mechanics and beyond.
In particular, we discuss a geometric quantization picture through the U(1)
central extension of the relativity group, which had been establish to work
well for the Galilean case but not for the Einstein case. We discuss
similarities and differences between our Poincar\'e-Snyder picture with a still
not fully understood $\sigma$ variable as the `evolution' parameter and some
use of an invariant time or the proper time parameter in some earlier
formulations with very similar mathematical structure. The study is a first
step towards the investigation of physics of the $\sigma$ variable at the
Poincar\'e-Snyder setting, plausible leading to experimental signatures to be
studied.
