form $$\left[\exp{\left\{\eta \left(x\frac{\partial}{\partial y} +
     y\frac{\partial}{\partial x}\right)\right\} } \right]
  \left[\exp{\left\{-\eta \left(p\frac{\partial}{\partial q} +
  q\frac{\partial}{\partial p}\right)\right\} }  \right] .$$ This exponential form squeezes the Wigner function of Eq.(\[wigf00\]) in the $x~y$ space as well as in their corresponding momentum space. However, in the momentum space, the squeeze is in the opposite direction as illustrated in Fig. \[ctran33\]. This is what we expect from canonical transformation in classical mechanics. Indeed, this corresponds to the unitary transformation which played the major role in Sec. \[2dim\].

Even though shown insignificant in Sec. \[2dim\], $K_{3}$ had a definite physical interpretation in Sec. \[dirac63\]. The transformation generated by $K_{3}$ takes the form $$\left[\exp{\left\{\eta \left(x\frac{\partial}{\partial q} +
     q\frac{\partial}{\partial x}\right)\right\} } \right]
  \left[\exp{\left\{\eta \left(y\frac{\partial}{\partial p} +
 p\frac{\partial}{\partial y}\right)\right\} }  \right] .$$ This performs the squeeze in the $x~q$ and $y~p$ spaces. In this case, the squeezes have the same sign, and the rate of increase is the same in all directions. We can thus have the same picture of squeeze for both $x~y$ and $p~q$ spaces as illustrated in Fig. \[ctran33\]. This parallel transformation corresponds to the Lorentz squeeze [@knp86; @kno79jmp].

As for the sheared state, the combination $$Q_{3} -  L_{2}  = -i\left( y\frac{\partial}{\partial x} +
q\frac{\partial}{\partial p} 