  We develop the approach of Felix Buot to construction of Wigner-Weyl calculus
for the lattice models. We apply this approach to the tight-binding models with
finite number of lattice cells. For simplicity we restrict ourselves to the
case of rectangular lattice. We start from the original Buot definition of the
symbol of operator. This definition is corrected in order to maintain
self-consistency of the algebraic constructions. It appears, however, that the
Buot symbol for simple operators does not have a regular limit when the lattice
size tends to infinity. Therefore, using a more dense auxiliary lattice we
modify the Buot symbol of operator in order to build our new discrete Weyl
symbol. The latter obeys several useful identities inherited from the continuum
theory. Besides, the limit of infinitely large lattice becomes regular. We
formulate Keldysh technique for the lattice models using the proposed Weyl
symbols of operators. Within this technique the simple expression for the
electric conductivity of a two dimensional non - equilibrium and non -
homogeneous system is derived. This expression smoothly approaches the
topological one in the limit of thermal equilibrium at small temperature and
large system area.
