But even for the pure Yang-Mills case (no fermions which couple to the gauge fields), there are various issues inherent to this approach: (i) problems in the direct simulation of dynamical processes (form factors at time-like momentum transfer, certain decay amplitudes) due to formulation of
lattice gauge theory in Euclidean space-time, (ii) finite-size scaling at finite temperature and its profound impact on infrared sensitive thermodynamical quantities, and (iii) customary simulations of the Euclidean Yang-Mills partition function subject to the Wilson discretization of the fundamental Yang-Mills action with the UV cutoff dependence (lattice spacing) and coarsening effects usually parameterized in terms of the perturbative Yang-Mills [beta] function.