variables $t$ and $s$ respectively. The fact that the squeeze and Lorentz transformations share the same mathematical formula is well known. However, the non-unitary operator $iK_{3}$ does not seem to have a space-time interpretation.

As for the sheared state, the generator can be written as $$Q_{3} - L_{2} ,$$ leading to the expression given in Eq.(\[shr07\]). This is a Hermitian operator leading to the unitary transformation of Eq.(\[shr05\]).

Entangled Oscillators in the Phase-Space Picture {#wigf}
================================================

Also in his 1963 paper, Dirac states that the Lie algebra of Eq. (\[dir12\]) can serve as the four-dimensional symplectic group $Sp(4)$. This group allows us to study squeezed or entangled states in terms of the four-dimensional phase space consisting of two position and two momentum variables [@hkn90; @knp91; @kn13].

![Transformations generated by $Q_{3}$ and $K_{3}$. As the parameter $\eta$ becomes larger, both the space and momentum distribution becomes larger. []{data-label="ctran33"}](ctran33b.eps)

In order to study the $Sp(4)$ contents of the coupled oscillator system, let us introduce the Wigner function defined as [@wig32] $$\begin{aligned}
\label{wigf01}
\lefteqn{W(x,y; p,q) = \left({1\over \pi} \right)^{2}
\int \exp \left\{- 2i (px' + qy') \right\} } \nonumber\\[3mm]
\mbox{ } & \mbox{ } & \mbox{ }
\times \psi^{*}(x + x', y + 