Lattice field theory fundamentals

Abstract

This chapter reviews the basic building blocks of the regularization of Quantum Field Theories (QFT) on a space-time lattice. It assumes some familiarity with QFT in the continuum. In an introductory section, the path integral formulation is reviewed, focusing on important aspects such as the transfer matrix, the relation of correlation functions and physical observables, the perturbative expansion, and the key issue of renormalization and the Wilsonian renormalization group. It then considers in detail the lattice formulation of scalar, fermion and gauge field theories, paying careful attention to their physical interpretation, and the continuum limit. The difficulty of discretizing chiral fermions is discussed in detail, and various fermion discretizations are described. The strong coupling expansion is introduced in the context of lattice Yang-Mills theory and the criteria for confinement and for the presence of a mass gap are presented. It concludes with a description of Wilson's formulation of lattice QCD and a brief overview of its applications.