Poincaré Symmetry from Heisenberg’s Uncertainty Relations

Başkal, Sibel
Kim , Young S.
Noz, Marilyn E
<jats:p>It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the S 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 S 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 S O ( 3 , 2 ) , it is possible to construct the inhomogeneous Lorentz group I S O ( 3 , 1 ) which serves as the fundamental symmetry group for quantum mechanics and quantum field theory in the Lorentz-covariant world. This I S O ( 3 , 1 ) group is commonly known as the Poincaré group.</jats:p>
Citation Formats
S. Başkal, Y. S. Kim, and M. E. Noz, “Poincaré Symmetry from Heisenberg’s Uncertainty Relations,” Symmetry, vol. 11, no. 3, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51652.