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Poincaré Symmetry from Heisenberg’s Uncertainty Relations
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Date
2019-3-20
Author
Başkal, Sibel
Kim , Young S.
Noz, Marilyn E
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<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>
Subject Keywords
Computer Science (miscellaneous)
,
Physics and Astronomy (miscellaneous)
,
Chemistry (miscellaneous)
,
General Mathematics
URI
https://hdl.handle.net/11511/51652
Journal
Symmetry
DOI
https://doi.org/10.3390/sym11030409
Collections
Department of Physics, Article