version 1.1 April 29, 2002 An Introduction to Lattice Gauge Theory Kurt Langfeld Institut f¨ ur Theoretische Physik, Universit¨atT¨ ubingen D–72076 T¨ ubingen, Germany Lecture presented at the European Graduate School Basel – T¨ ubingen, Basel, 22.4.–26.4.2002 Abstract An introduction into the subject of critical phenomena in the con- text of solid state physics is presented. It is shown that the physics of a classical lattice model is described in terms of a quantum field theory in the vicinity of a (continuous) phase transition. It is explained how in practice the numerical simulation of a lattice model can be used to access the information on the QFT. Subsequently, the lecture focuses onto Yang-Mills theory and to some extent onto QCD, the theory of strong interactions. The lattice version of non-abelian Yang-Mills the- ory is constructed. It is shown how the continuum limit is approached in practical simulations. Finally, I review recent findings obtained by lattice gauge calculations: among others, the issue of quark confine- ment is addressed, and a brief summary of the information on the high temperature phase of QCD is presented. The latter topic is highly rel- evant to understand the properties of the quark gluon plasma (RHIC physics). email: kurt.langfeld@uni-tuebingen.de www: http://solid13.tphys.physik.uni-tuebingen.de/ 1