## Lattice Gauge Theories: An IntroductionThis 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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### Common terms and phrases

abelian algorithm analogous anomaly axial vector current calculate chapter chiral symmetry colour compute configuration Consider continuum formulation correlation function corresponding coupling constant defined degrees of freedom denote dependence derivative determined Diagrams contributing dimensioned dimensionless Dirac discussed divergence dynamics energy sum rule ensemble average equation euclidean expectation value factor Feynman integrals field theory finite temperature gauge field gauge invariant gauge potentials gauge theory gauge transformation given glueball gluon Grassmann Green functions hadron Hamiltonian Hence integrand lattice action lattice formulation lattice gauge theories lattice QCD lattice regularized lattice sites lattice units link variables matrix measured in lattice momenta momentum space Monte Carlo naive continuum limit non-abelian obtained partition function path integral perturbation theory physical plaquette propagator quantum quark masses renormalization replaced screening mass shown in fig simulations space-time spatial string tension strong coupling SU(N term vanishing Ward identity Wilson fermions Wilson loop