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.
Dedication
Preface
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
1.INTRODUCTION
2.THE PATH INTEGRAL APPROACH TO QUANTIZATION
2.1The Path Integral Method in Quantum Mechanics
2.2 Path Integral Representation of Bosonic Green FunctionsinFieldtheory
2.3The Transfer Matrix
2.4 Path Integral R，epresentation of FermionicGreen Functions
2.5Discretizing Space—Time.The Lattice as a Regulator ofaQuantum Field Theory
3.THE FREE SCALAR FIELD ON THE LATTICE
4.FERMIONS ON THE LATTICE
4.1The Doubling Problem
4.2A Closer Look at Fermion Doubling
4.3Wilson Fermions
4.4Staggered Fermions
4.5 Technical Details of the Staggered Fermion Formulation
4.6 Staggered Fermions in Momentum Space
4.7Ginsparg—Wilson Fermions.The Overlap Operator
5.ABELIAN GAUGE FIELDS ON THE LATTICEAND COMPACT QED
5.1 Preliminaries
5.2 Lattice Formulation of QED
6.NON ABELIAN GAUGE FIELDS ON THE LATTICECOMPACT QCD
7.THE WILSON LOOP AND THE STATICQUARK—ANTIQUARK POTENTIAL
7.1A Look at Non—Relativistic Quantum Mechanics
7.2 The Wilson Loop and the Static qq=Potentialin QED
7.3 The Wilson Loop in QCD
8.THE QQ—POTENTIAL IN SOME SIMPLE MODELS
8.1The Potentialin Quenched QED
8.2The Potential in Quenched Compact QED2
9.THE CONTINUUM LIMIT OF LATTICE QCD
9.1 Critical Behaviour of Lattice QCD and the ContinuumLimit
9.2 Dependence of the Coupling Constant on the Lattice Spacingand the Renormalization Group β—Function
10.LATTICE SUM RULES
10.1 Energy Sum Rule for the Harmonic Oscillator
10.2 The SU（N） Gauge Action on an Anisotropic Lattice
10.3 Sum Rules for the Static qq—Potential
10.4Determination of the Electric， Magnetic and Anomalous Contribution to the qq Potential
10.5 Sum Rules for the Glueball Mass
11.THE STRONG COUPLING EXPANSION
11.1The qq—Potential to Leading Order in Strong Coupling
11.2 Beyond the Leading Approximation
11.3The Lattice Hamiltonian in the Strong Coupling Limitand the String Picture of Confinement
12.THE HOPPING PARAMETER EXPANSION
12.1Path Integral R，epresentation of Correlation Functionsin Terms of Bosonic Variables
12.2Hopping Parameter Expansion of the Fermion Propagatorin an ExternalField
12.3Hopping Parameter Expansion of the Effective Action
12.4 The HPE and the Pauli Exclusion Principle
13.WEAK COUPLING EXPANSION （Ⅰ）.THE φ3—THEORY
13.1Introduction
13.2 Weak Coupling Expansion of Correlation Functions in the φ3—Theory
13.3 The Power Counting Theorem of Reisz
14.WEAK COUPLING EXPANSION （Ⅱ）.LATTICE QED
14.1 The Gauge Fixed Lattice Action
14.2 Lattice Feynman Rules
14.3Renormalization of the Axial Vector Current in One—LoopOrder
14.4The ABJ Anomaly
15.WEAK COUPLING EXPANSION （Ⅲ）.LATTICE QCD
15.1The Link Integration Measure
15.2 Gauge Fixing and the Faddeev—Popov Determinant
15.3 The Gauge Field Action
15.4 Propagators and Vertices
15.5 Relation between AL and the A—Parameter of Continuum QCD
15.6Universality of the Axial Anomaly in Lattice QCD
16.MONTE CARLO METHODS
16.1Introduction
16.2 Construction Principles for Algorithms.Markov Chains
16.3 The Metropolis Method
16.4 The Langevin Algorithm
16.5 The Molecular Dynamics Method
16.6 The Hybrid Algorithm
16.7 The Hybrid Monte Carlo Algorithm
16.8 The Pseudofermion Method
16.9Application of the Hybrid Monte Carlo Algorithmto Systems with Fermions
17.SOME RESULTS OF MONTE CARLO CALCULATIONS
17.1 The String Tension and the qq Potentialin the SU（3） GaugeTheory
17.2 The qq—Potentialin Full QCD
17.3 Chiral Symmetry Breaking
17.4Glueballs
17.5 Hadron Mass Spectrum
17.6Instantons
17.7 Flux Tubes in qq and qqq—Systems
17.8The Dual Superconductor Picture of Confinement
17.9 Center Vortices and Confinement
17.10 Calorons
18.PATH—INTEGRAL REPRESENTATION OF THE THERMODYNAMICAL PARTITION FUNCTIONFOR SOME SOLVABLE BOSONIC AND FERMIONICSYSTEMS
18.1Introduction
18.2Path—Integral R；epresentation of the Partition Function in Quantum Mechanics
18.3 Sum Rule for the Mean Energy
18.4 Test of the Energy Sum Rule.The Harmonic Oscillator
18.5The Free Relativistic Boson Gas in the Path Integral Approach
18.6The Photon Gas in the Path Integral Approach
18.7 Functional Methods for Fermions.Basics
18.8Path Integral R，epresentation of the Partition Functionfor a Fermionic System valid for Arbitrary Time—Step
18.9 A Modified Fermion Action Leading to Fermion Doubling
18.10The Free Dirac Gas.Continuum Approach
18.11 Dirac Gas of Wilson Fermions on the Lattice
……
19.FIMTE TEMPERATURE PERTURBATION THEORY OFAND ON THE LATTICE
20.NON—PERTURBATIVE QCD AT FINITE TEMPERATURE
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Appendix G
References
Index
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