ABSTRACT
This chapter provides an elementary introduction to lattice field theory in general, including some important insights that it generates concerning the renormalization group. It discusses how simple field theories are discretized; scalar fields, fermion fields, and gauge fields each require their own prescriptions. The chapter explores the physics of renormalization and of the RGE from a lattice/statistical mechanics perspective, before returning to QCD. Having explored the discretization of actions for free scalars and Dirac fermions, it shows how to implement gauge invariance on the lattice. The chapter provides a brief introduction to this formalism, starting with quantum mechanics. It describes lattice QCD, with a brief survey of some of the impressive results now being obtained numerically.
