Poincaré Symmetry from Heisenberg’s Uncertainty Relations
Poincaré Symmetry from Heisenberg’s Uncertainty Relations
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 …