LINEAR CANONICAL-TRANSFORMATIONS OF COHERENT AND SQUEEZED STATES IN THE WIGNER PHASE-SPACE .3. 2-MODE STATES

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 Schrödinger picture, appears as Diracs 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. © 1990 The American Physical Society.