Lattice Gauge Theories: An Introduction

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World Scientific, 2005 - Science - 588 pages
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.
 

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Contents

INTRODUCTION
1
THE PATH INTEGRAL APPROACH TO QUANTIZATION
7
THE FREE SCALAR FIELD ON THE LATTICE
36
FERMIONS ON THE LATTICE
43
PATHINTEGRAL REPRESENTATION OF
44
ABELIAN GAUGE FIELDS ON THE LATTICE
77
NONABELIAN GAUGE FIELDS ON THE LATTICE
87
THE WILSON LOOP AND THE STATIC
95
THE STRONG COUPLING EXPANSION
151
THE HOPPING PARAMETER EXPANSION
170
WEAK COUPLING EXPANSION I THE 3THEORY
192
WEAK COUPLING EXPANSION II LATTICE QED
209
WEAK COUPLING EXPANSION III LATTICE QCD
242
MONTE CARLO METHODS
284
SOME RESULTS OF MONTE CARLO CALCULATIONS
317
FINITE TEMPERATURE PERTURBATION THEORY
424

THE QQ POTENTIAL IN SOME SIMPLE MODELS
109
THE CONTINUUM LIMIT OF LATTICE QCD
119
LATTICE SUM RULES
130
NONPERTURBATIVE QCD AT FINITE
485
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