This book introduces a number of topics in lattice gauge theories, including analytical as well as numerical computational methods and a discussion of modern developments in finite temperature QCD. It aims to provide young physicists with the necessary background and basic computational tools to understand the published literature and to carry out research on their own. All technicalities are avoided. Nevertheless, sufficient details are given, so that the reader can follow the extensive literature on the subject without too much effort and is able to fill in the technical details with the help of the cited literature. This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in quantum field theory.
The path integral approach to quantization; the free scalar field on the lattice; fermions on the lattice; Abelian gauge fields on the lattice and compact QED; non Abelian gauge fields on the lattice and compact QCD; the Wilson-Wegner loop and the static Quark-Antiquark potential; the QQ-potential in some simple models; the continuum limit of lattice QCD; the strong coupling expansion; the weak coupling expansion I - the ph4-theory; weak coupling expansion II - lattice QED; weak coupling expansion III - lattice QCD; the hopping parameter expansion; Monte Carlo methods; some Monte Carlo results in quenched QCD; some recent MC results in full QCD; an introduction to finite temperature continuum field theory - the ph4-theory; lattice formulation of QCD at finite temperature; MC study of the deconfinement phase transition; the high temperature phase of QCD.