Lattice Methods for Quantum ChromodynamicsNumerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology.This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually doing a simulation, descriptions of common strategies to connect simulation results to predictions of physical quantities, and a discussion of uncertainties in lattice simulations. More importantly, while lattice QCD is a well-defined field in its own right, it has many connections to continuum field theory and elementary particle physics phenomenology, which are carefully elucidated in this book. /remove |
Contents
1 Introduction | 1 |
2 Continuum QCD and its phenomenology | 5 |
3 Path integration | 33 |
4 Renormalization and the renormalization group | 61 |
5 YangMills theory on the lattice | 87 |
6 Fermions on the lattice | 101 |
7 Numerical methods for bosons | 143 |
8 Numerical methods for fermions | 155 |
11 Spectroscopy | 215 |
12 Lattice perturbation theory | 235 |
13 Operators with anomalous dimension | 249 |
14 Chiral symmetry and lattice simulations | 261 |
15 Finite volume effects | 279 |
16 Testing the standard model with lattice calculations | 295 |
17 QCD at high temperature and density | 317 |
| 329 | |
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Common terms and phrases
algorithm amplitude approximation axial baryon chiral symmetry clover coefficients color components compute construct continuum limit correlator coupling constant cutoff decay defined derivative dimension dimensional Dirac operator discrete effective field theory eigenmodes eigenvalues equation Euclidean example expectation value factor fat links fermion action fermion determinant Feynman finite flavor gauge configuration gauge field gauge theory glueball gluon Goldstone boson graphs Grassmann Green's functions hadronic Hamiltonian heavy quark hermitian hypercube improvement interactions interpolating operators Lagrangian lattice action lattice calculation lattice QCD linear low energy Lüscher massless matrix element meson method molecular dynamics momenta momentum multiplet nonperturbative parameters particle partition function path integral perturbation theory physical pion plaquette problem propagator pseudoscalar quark mass quark model renormalization group replaced result scale simulation singlet spatial spin staggered fermions tadpole taste term transformation vacuum variables wave function Wilson fermions Wilson loop zero modes ημ μν