## Quarks, Gluons and LatticesThis book introduces the lattice approach to quantum field theory. The spectacular successes of this technique include compelling evidence that exchange of gauge gluons can confine the quarks within subnuclear matter. The lattice framework enables novel schemes for quantitative calculation and has caused considerable cross-disciplinary activity between elementary particle and solid state physicists. The treatment begins with the lattice definition of a path integral and ends on Monte Carlo simulation methods. Other topics include invariant group integration, duality, mean field theory and renormalization group techniques. The reader is assumed to have a basic background in relativistic quantum mechanics and some exposure to gauge theories. |

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### Contents

Quarks and gluons | 1 |

Lattices | 5 |

Path integrals and statistical mechanics | 8 |

Scalar fields | 14 |

Fermions | 20 |

Gauge fields | 29 |

Lattice gauge theory | 34 |

Group integration | 39 |

Asymptotic freedom and dimensional transmutation | 88 |

Mean field theory | 94 |

The Hamiltonian approach | 101 |

Discrete groups and duality | 108 |

MigdalKadanoff recursion relations | 117 |

Monte Carlo simulation I the method | 127 |

Monte Carlo simulation II measuring observables | 140 |

Beyond the Wilson action | 151 |

Gaugeinvariance and order parameters | 51 |

Strong coupling | 60 |

Weak coupling | 77 |

Renormalization and the continuum limit | 81 |

162 | |

167 | |

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### Common terms and phrases

action algorithm analysis appears approximation associated becomes begin calculation chapter confinement connection consider constant continuum limit corresponding Creutz critical cutoff define dependence derivative determinant diagram dimensions direction discussed effects energy equation evaluate example expansion expectation expression factor fermionic field field theory figure finite fixed formulation function gauge group gauge theory given gives Hamiltonian identity indices integral interactions introduce invariant lattice lattice gauge theory lattice spacing lines loop mass matrix mean measure mechanics Monte Carlo normalization Note observables obtain occurs operators parameter particle particular perturbative phase transition physical plaquette potential prediction problem quantum quantum mechanical quark relation renormalization representation represents result scale simple sources space statistical strong coupling symmetry temperature transformation usual vanishes variables weak coupling Wilson zero