1 From Monte Carlo Integration to Lattice Quantum Chromo Dynamics

Lectures on Lattice Field Theory and Lattice QCD given at the Graduate Students Association (GSA) Summer School (Fermilab). In these lectures we provide a short introduction to the Monte Carlo integration method and its applications. We show how the origin of ultraviolet divergences if Field Theories is in the undefined formal product of distributions and how one can define the Path Integral in terms of regularized distributions in order to cancel these divergences. This technique provides the only non perturbative regularization procedure of continuum Field Theories and, at the same time, provides a practical method to compute correlation (Green) functions (using Monte Carlo integration for the regularized path integrals). We then apply these tools to formulate QCD on a lattice. Some of the examples are accompanied by complete computer programs. Freely download libraries and examples from: http://latticeqcd.fnal.gov/software/fermiqcd/