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Physics Letters A

Squeezed states and thermally excited states in the wigner phase-space picture of quantum mechanics

Y.S. Kim, Ming Li

Published Aug 1, 1989• 17 citations
Publisher
DOI
10.1016/0375-9601(89)90942-0

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It is shown that the basic symmetry of two-mode squeezed states is governed by the group Sp(4) in the Wigner phase space which is locally isomorphic to the (3+2)-dimensional Lorentz group. This symmetry, in the Schr\"odinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.