  It is noted that the single-variable Heisenberg commutation relation contains
the symmetry of the $Sp(2)$ group which is isomorphic to the Lorentz group
applicable to one time-like dimension and two space-like dimensions, known as
the $O(2,1)$ group. According to Paul A. M. Dirac, from the uncertainty
commutation relations for two variables, it possible to construct the de Sitter
group $O(3,2)$, namely the Lorentz group applicable to three space-like
variables and two time-like variables. By contracting one of the time-like
variables in $O(3,2)$, it is possible, to construct the inhomogeneous Lorentz
group $IO(3,1)$ which serves as the fundamental symmetry group for quantum
mechanics and quantum field theory in the Lorentz covariant world. This
$IO(3,1)$ group is commonly known as the Poincar\'e group.
