Quantum fields on a lattice / István Montvay, Gernot Münster

Includes bibliographical references and index

Contents Preface 1 Introduction 1.1 Historical remarks 1.2 Path integral in quantum mechanics 1.3 Euclidean quantum field theory 1.4 Euclidean functional integrals 1.5 Quantum field theory on a lattice 1.6 Continuum limit and critical behaviour 1.7 Renormalization group equations 1.8 Thermodynamics of quantum fields 2 Scalar fields 2.1 [phi [superscript 4]] model on the lattice 2.2 Perturbation theory 2.3 Hopping parameter expansions 2.4 Luscher-Weisz solution and triviality of the continuum limit 2.5 Finite-volume effects 2.6 N-component model 3 Gauge fields 3.1 Continuum gauge fields 3.2 Lattice gauge fields and Wilson's action 3.3 Perturbation theory 3.4 Strong-coupling expansion 3.5 Static quark potential 3.6 Glueball spectrum 3.7 Phase structure of lattice gauge theory 4 Fermion fields 4.1 Fermionic variables 4.2 Wilson fermions 4.3 Kogut-Susskind staggered fermions 4.4 Nielsen-Ninomiya theorem and mirror fermions 4.5 QED on the lattice 5 Quantum chromodynamics 5.1 Lattice action and continuum limit 5.2 Hadron spectrum 5.3 Broken chiral symmetry on the lattice 5.4 Hadron thermodynamics 6 Higgs and Yukawa models 6.1 Lattice Higgs models 6.2 Lattice Yukawa models 7 Simulation algorithms 7.1 Numerical simulation and Markov processes 7.2 Metropolis algorithms 7.3 Heatbath algorithms 7.4 Fermions in numerical simulations 7.5 Fermion algorithms based on differential equations 7.6 Hybrid Monte Carlo algorithms 7.7 Cluster algorithms 8 Appendix 8.1 Notation conventions and basic formulas References Index