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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 a great number of figures. Beyond the necessary amendments and slight extensions of some sections in the third edition, the fourth edition includes an expanded section on Calorons a subject which has been under intensive investigation during the last twelve years.
List of 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 ?3-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.
