  We consider symplectic quaternions instead of unitary spinors sitting on a
lattice, and calculate the fixed point Wilson action on a finite $2D$ plane
expanded by $u_1 a e_1+ u_2 a e_2$ and on two $2D$ planes separated by $a
e_1\wedge e_2$. Only the nearlest neighbor interactions are considered.
Following Migdal and Kadanoff, we perform the renormalization of the Wilson
action by making the lattice spacing $(\frac{1}{2})^{h}a$ $(h=0,\cdots,11 )$,
in order to simulate bosonic and solitonic phonon propagation in materials.
Renormalization group method of Benfatto and Gallavotti for $(2+1)D$ scalar
$\phi^4$ system for sound propagation in Fermi sea is applied and feasibility
of numerical simulation is discussed.
