Introduction to Lattice QCD

In this chapter we give a brief introduction to Quantum Chromodynamics, the fundamental theory of strong interactions, and its discretization on a four-dimensional hypercubic grid. We discuss the requirements imposed by gauge symmetry and translate them on the lattice. We identify the fermion fields as living on the lattice sites and the gauge fields on the lattice links. We briefly introduce the problem of fermion doubling on the lattice. Finally, we discuss Monte Carlo techniques and give an example of importance sampling algorithms. For books and reviews on the topic we recommend (Rothe (1992) World Sci Lect Notes Phys 43:1–381; Smit (2002) Camb Lect Notes Phys 15:1–271).