Chapter 5
QCD on the Lattice
Hartmut Wittig
5.1 Introduction and Outline
Since Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum
Chromodynamics has become increasingly important for the study of the strong
interaction at low energies, and has now turned into a mature and established
technique. In spite of the fact that the lattice formulation of Quantum Field Theory
has been applied to virtually all fundamental interactions, it is appropriate to discuss
this topic in a chapter devoted to QCD, since by far the largest part of activity is
focused on the strong interaction. Lattice QCD is, in fact, the only known method
which allows ab initio investigations of hadronic properties, starting from the QCD
Lagrangian formulated in terms of quarks and gluons.
5.1.1 Historical Perspective
In order to illustrate the wide range of applications of the lattice formulation, we
give a brief historical account below.
First applications of the lattice approach in the late 1970s employed analytic
techniques, predominantly the strong coupling expansion, in order to investigate
colour confinement and also the spectrum of glueballs. While these attempts gave
valuable insights, it soon became clear that in the case of non-Abelian gauge theories
such expansions were not sufficient to produce quantitative results.
H. Wittig ()
Johannes-Gutenberg-Universität Mainz, Mainz, Germany
e-mail: hartmut.wittig@uni-mainz.de
© The Author(s) 2020
H. Schopper (ed.), Particle Physics Reference Library,
https://doi.org/10.1007/978-3-030-38207-0_5
137
QCD on the Lattice
Hartmut Wittig
5.1 Introduction and Outline
Since Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum
Chromodynamics has become increasingly important for the study of the strong
interaction at low energies, and has now turned into a mature and established
technique. In spite of the fact that the lattice formulation of Quantum Field Theory
has been applied to virtually all fundamental interactions, it is appropriate to discuss
this topic in a chapter devoted to QCD, since by far the largest part of activity is
focused on the strong interaction. Lattice QCD is, in fact, the only known method
which allows ab initio investigations of hadronic properties, starting from the QCD
Lagrangian formulated in terms of quarks and gluons.
5.1.1 Historical Perspective
In order to illustrate the wide range of applications of the lattice formulation, we
give a brief historical account below.
First applications of the lattice approach in the late 1970s employed analytic
techniques, predominantly the strong coupling expansion, in order to investigate
colour confinement and also the spectrum of glueballs. While these attempts gave
valuable insights, it soon became clear that in the case of non-Abelian gauge theories
such expansions were not sufficient to produce quantitative results.
H. Wittig ()
Johannes-Gutenberg-Universität Mainz, Mainz, Germany
e-mail: hartmut.wittig@uni-mainz.de
© The Author(s) 2020
H. Schopper (ed.), Particle Physics Reference Library,
https://doi.org/10.1007/978-3-030-38207-0_5
137