  We rewrite various lattice Hamiltonian in condensed matter physics in terms
of U(2/2) operators that we introduce. In this representation the symmetry
structure of the models becomes clear. Especially, the Heisenberg, the
supersymmetric t-J and a newly proposed high-$T_c$ superconducting Hamiltonian
reduce to the same form $H=$$-t\sum_{<jk>}\sum_{ac}X^{ac}_j X^{ca}_k
(-1)^{F(c)}$. This representation also gives us a systematic way of searching
for the symmetries of the system.
