ABSTRACT
This Chapter provides an elementary introduction to Lattice QCD calculations, a field which has represented, over the last decades, an efficient tool for calculating the hadron mass spectrum and a variety of hadronic amplitudes relevant for phenomenology. The simplest gluon and quark lattice actions introduced by K. Wilson are discussed in some detail. Reference is provided to other lattice actions, such as the Twisted Fermions, Staggered Fermions and Domain Wall regularisations, also employed in recent calculations. The Wilson lattice QCD action for fermions conflicts with the naive conservation of the axial currents. It is argued that such a conflict is necessary if lattice QCD has to reproduce, in the continuum limit, the correct chiral anomalies needed e.g. for https://www.w3.org/1998/Math/MathML" display="inline"> π 0 → γ γ decay. Prescriptions are illustrated to insure that indeed chiral symmetry is recovered in the continuum limit, except for the flavour singlet axial currents, where continuum anomalies have indeed been observed. The construction of lattice Green's functions is described, with reference to a recent, most successful, computation of the mass spectrum of the light hadrons. The remarkable evolution of computing power, from 1 Gigaflop ( https://www.w3.org/1998/Math/MathML" display="inline"> 10 9 operations/sec ) in the years 1980 to the border of 1 Exaflop ( https://www.w3.org/1998/Math/MathML" display="inline"> 10 18 operations/sec ) of present times, is illustrated, which is the basis of the most advanced results in lattice QCD calculations, reported in Chapters 18 and 19.
