$$\begin{aligned}
\label{sqphase}
K_{1} &=& -{i\over 2}\left\{\left( x{\partial \over \partial p} +
p{\partial \over \partial x} \right) -
\left(y{\partial \over \partial q} +
q{\partial \over \partial y} \right)\right\}, \nonumber \\[3mm]
K_{2} &=& -{i\over 2}\left\{\left(x{\partial \over \partial x} +
  y{\partial \over \partial y}\right) -
  \left(p{\partial \over \partial p} +
  q{\partial \over \partial q}\right)\right\} , \nonumber \\[3mm]
K_{3} &=& +{i\over 2}\left\{\left(x{\partial \over \partial q} +
  q{\partial \over \partial x}\right) +
  \left(y{\partial \over \partial p} +
  p{\partial \over \partial y}\right)\right\} , \nonumber \\[3mm]
Q_{1} &=& +{i\over 2}\left\{\left(x{\partial \over \partial x} +
  q{\partial \over \partial q}\right) -
  \left(y{\partial \over \partial y} +
  p{\partial \over \partial p}\right)\right\} ,\nonumber \\[3mm]
Q_{2} &=& -{i\over 2}\left\{\left(x{\partial \over \partial p} +
  p{\partial \over \partial x}\right) +
  \left(y{\partial \over \partial q} +
  q{\partial \over \partial y}\right)\right\} ,\nonumber \\[3mm]
Q_{3} &=& -{i\over 2}\left\{\left(y{\partial \over \partial x} +
  x{\partial \over \partial y} \right) -
  \left(q{\partial \over \partial p} + p{\partial \over
  \partial q}\right)\right\} .\end{aligned}$$ These generators also satisfy the Lie algebra given in Eq.(\[dir10\]) and Eq.(\[dir12\]). Transformations generated by these generators have been discussed in the literature [@hkn90; @hkn95jmp; @kn13].

As in the case of Sec. \[dirac63\], we are interested in the generators $Q_{3}$ and $K_{3}$. The transformation generated by $Q_{3}$ takes the 