Wigner - Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

Understand

We develop Wigner - Weyl formalism for the lattice models.

• For the definiteness we consider Wilson fermions in the presence of $U(1)$ gauge field.
• The given technique reduces calculation of the two point fermionic Green function to solution of the Groenewold equation.
• It relates Wigner transformation of the Green function with the Weyl symbol $Q_W$ of Wilson Dirac operator.