Noninertial symmetry group with invariant Minkowski line element consistent with Heisenberg quantum commutation relations

6th International Symposium on Quantum Theory and Symmetries

Low, Stephen G.

关键词: Automorphism groups;    Central extensions;    Classical limits;    Commutation relation;    Heisenberg algebras;    Quantum system;    Symmetry groups;    Symplectic groups;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/462/1/012032/pdf
DOI  :  10.1088/1742-6596/462/1/012032

来源: IOP

【 摘 要 】

The maximal symmetry of a quantum system with Heisenberg commutation relations is given by the projective representations of the automorphism group of the Weyl-Heisenberg algebra. The automorphism group is the central extension of the inhomogeneous symplectic group with a conformal scaling that acts on extended phase space. We determine the subgroup that also leaves invariant a degenerate Minkowski orthogonal line element. This defines noninertial relativistic symmetry transformations that have the expected classical limit as c → ∞.