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 2.1 The Path Integral Method in Quantum Mechanics 2.2 Path Integral Representation of Bosonic Green Functions inFieldtheory 2.3 The Transfer Matrix 2.4 Path Integral R,epresentation of Fermionic Green Functions 2.5 Discretizing Space-Time.The Lattice as a Regulator ofa Quantum Field Theory 3.THE FREE SCALAR FIELD ON THE LATTICE 4.FER,MIONS ON THE LATTICE 4.1 The Doubling Problem 4.2 A Closer Look at Fermion Doubling 4.3 Wilson Fermions 4.4 Staggered Fermions 4.5 Technical Details of the Staggered Fermion Formulation 4.6 Staggered Fermions in Momentum Space 4.7 Ginsparg-Wilson Fermions.The Overlap Operator 5.ABELIAN GAUGE FIELDS ON THE LATTICE AND PACT QED 5.1 Preliminaries 5.2 Lattice Formulation of QED …… 6.NON ABELIAN GAUGE FIELDS ON THE LATTICE PACT QCD 7.THE WILSON LOOP AND THE STATIC QUARK-ANTIQUARK POTENTIAL 8.THE POTENTIAL IN SOME SIMPLE MODELS 9.THE CONTINUUM LIMIT OF LATTICE QCD 10.LATTICE SUM RULES 11.THE STRONG COUPLING EXPANSION 12.THE HOPPING PARAMETER EXPANSION 13.WEAK COUPLING EXPANSION (I).THE φ3_THEORY 14.WEAK COUPLING EXPANSION (II).LATTICE QED 15.WEAK COUPLING EXPANSION (III).LATTICE QCD 16.MONTE CARLO METHODS 17.SOME RESULTS OF MONTE CARLO CALCULATIONS 18.PATH-INTEGRAL REPRESENTATION OF THE THERMODYNAMICAL PARTITION FUNCTION FOR SOME SOLVABLE BOSONIC AND FERMIONIC SYSTEMS 19.FINITE TEMPERATURE PERTURBATION THEORY OFF AND ON THE LATTICE 20.NON-PERTURBATIVE QCD AT FIBfITE TEMPERATURE
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