Non-perturbative QCD by lattice simulations

Nowadays, Quantum ChromoDynamics is accepted as the quantum field theory which describes strong interactions. Asymptotic freedom guarantees the applicability of a perturbative expansion at energies much larger than ΛQCD ∼ 200 MeV. At low energies, instead, the theory is non-perturbative: the only known computational scheme of the theory in this regime was proposed by K. G. Wilson more than 30 years ago [1] and is based on a Monte Carlo stochastic computation of the path integral of the theory, regularized in a gauge invariant on an Euclidean space-time lattice. Let us consider the partition function of QCD at finite temperature T on a finite spatial volume V . That can be given a regularized path integral representation as follows: