On the numerical computation of Q.C.D. mass spectrum: an introduction

Exploiting MC techniques for analyzing a lattice gauge theory coupled to fermionic matter fields, we just quote here the 3 main difficulties: first the anticommuting character of the fermionic fields, implying a strong non locality of the effective action, obtained by integrating out the fermionic fields. The second point is that the bare quark mass is not allowed, on a finite lattice, to be arbitrarily small: it is controlling the correlation length of the fermionic sector of the theory. The possible way out consists in working with unphysically large quark masses, and eventually trying to extrapolate. Last we have to face the so called doubling problem: the discretization of the continuum theory makes a number of unwanted fermionic species appearing, and/or explicitly breaks the chiral invariance of the theory