The new definition of lattice gauge fields and the Landau gauge

and it is more natural as an averaged gauge field on the link in the continuum theory. We use the analytic method of eigenspace projection operator together with Cardano’s eigenvalue solver for transformation between U and A. It is remarkable that the definition (1) of gauge field allows the same type of formulation of the lattice Landau or Coulomb gauge condition as the continuum theory, i.e., minimizing condition of ‖A‖ along the gauge orbits[3,4]. The definion A = logU requires a proper choice of branch for traceless A, and A becomes a nonanalytic function of U , and yet ‖A‖ still remains a continuous function of U . This fact justifies the existence of the global minimum of ‖A‖ along the gauge orbit (the minimal Landau gauge condition). The gauge transformation is