This book provides a broad introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD. It serves as a textbook for advanced graduate students, and also provides the reader with the necessary analytical and numerical techniques to carry out research on his own. Although the analytic calculations are sometimes quite demanding and go beyond an introduction, they are discussed in sufficient detail, so that the reader can fill in the missing steps. The book also introduces the reader to interesting problems which are currently under intensive investigation. Whenever possible, the main ideas are exemplified in simple models, before extending them to realistic theories. Special emphasis is placed on numerical results obtained from pioneering work. These are displayed in numerous figures.

Contents:

• 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. Compact QCD
• The Wilson Loop and the Static Quark–Antiquark Potential
• The QQ Potential in Some Simple Models
• The Continuum Limit of Lattice QCD
• Lattice Sum Rules
• The Strong Coupling Expansion
• The Hopping Parameter Expansion
• Weak Coupling Expansion (I). The Φ³-Theory
• Weak Coupling Expansion (II). Lattice QED
• Weak Coupling Expansion (III). Lattice QCD
• Monte Carlo Methods
• Some Results of Monte Carlo Calculations
• Path-Integral Representation of the Thermodynamical Partition Function for Some Solvable Bosonic and Fermionic Systems
• Finite Temperature Perturbation Theory Off and On the Lattice
• Non-Perturbative QCD at Finite Temperature.

“This book is clearly written and its content is explained so as to be understandable by anyone with a knowledge of the basics of quantum field theory. As an introductory text, it concentrates more on physical motivation and general principles, often avoiding more mathematically rigorous proofs where they might be confusing to the beginner ... it acts as a valuable starting point for anyone wishing to understand more about this subject.”

“This book is of invaluable interest for scientists working in this area (gauge theories on lattices) and it is addressed mainly at the graduate students interested in particle physics. It can be also of interest for physicists working in statistical mechanics, since the lattice formulation of field theories resembles closely that of complex mechanical systems.”