Lattice methods for quantum chromodynamics / Thomas DeGrand, Carleton DeTar.

Format:

Book

Author/Creator:

DeGrand, T. (Thomas)

Contributor:

DeTar, Carleton.

Language:

English

Subjects (All):

Lattice gauge theories--Mathematical models.

Lattice gauge theories.

Quantum chromodynamics--Mathematical models.

Quantum chromodynamics.

Physical Description:

1 online resource (xv, 345 p. ) ill.

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, c2006.

Language Note:

English

Summary:

Numerical 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.

Contents:

Preface

1. Introduction

2. Continuum QCD and its phenomenology. 2.1. The Lagrangian and QCD at short distance. 2.2. The nonrelativistic quark model. 2.3. Heavy quark systems. 2.4. Chiral symmetry and chiral symmetry breaking. 2.5. A technical aside: Ward identities. 2.6. The axial anomaly and instantons. 2.7. The large N[symbol] limit

3. Path integration. 3.1. Lattice Schwinger model. 3.2. Hamiltonian with gauge fields. 3.3. Feynman path integral. 3.4. Free fermions. 3.5. The interacting theory

4. Renormalization and the renormalization group. 4.1. Blocking transformations. 4.2. Renormalization group equations. 4.3. Renormalization group equations for the scalar field. 4.4. Effective field theories

5. Yang-Mills theory on the lattice. 5.1. Gauge invariance on the lattice. 5.2. Yang-Mills actions. 5.3. Gauge fixing. 5.4. Strong coupling

6. Fermions on the lattice. 6.1. Naive fermions. 6.2. Wilson-type fermions. 6.3. Staggered fermions. 6.4. Lattice fermions with exact chiral symmetry. 6.5. Exact chiral symmetry from five dimensions. 6.6. Heavy quarks

7. Numerical methods for bosons. 7.1. Importance sampling. 7.2. Special methods for the Yang-Mills action

8. Numerical methods for fermions. 8.1. Taming the fermion determinant: the [symbol] algorithm. 8.2. Taming the fermion determinant: the R algorithm. 8.3. The fourth root approximation. 8.4. An exact algorithm for the fourth root: rational hybrid Monte Carlo. 8.5. Refinements. 8.6. Special considerations for overlap fermions. 8.7. Monte Carlo methods for fermions. 8.8. Conjugate gradient and its relatives

9. Data analysis for lattice simulations. 9.1. Correlations in simulation time. 9.2. Correlations among observables. 9.3. Fitting strategies

10. Designing lattice actions. 10.1. Motivation. 10.2. Symanzik improvement. 10.3. Tadpole improvement. 10.4. Renormalization-group inspired improvement. 10.5. "Fat link" actions

11. Spectroscopy. 11.1. Computing propagators and correlation functions. 11.2. Sewing propagators together. 11.3. Glueballs. 11.4. The string tension

12. Lattice perturbation theory. 12.1. Motivation. 12.2. Technology. 12.3. The scale of the coupling constant

13. Operators with anomalous dimension. 13.1. Perturbative techniques for operator matching. 13.2. Nonperturbative techniques for operator matching

14. Chiral symmetry and lattice simulations. 14.1. Minimal introduction to chiral perturbation theory. 14.2. Quenching, partial quenching, and unquenching. 14.3. Chiral perturbation theory for staggered fermions. 14.4. Computing topological charge

15. Finite volume effects. 15.1. Finite volume effects in chiral perturbation theory. 15.2. The [symbol]-regime. 15.3. Finite volume, more generally. 15.4. Miscellaneous comments

16. Testing the standard model with lattice calculations. 16.1. Overview. 16.2. Strong renormalization of weak operators. 16.3. Lattice discrete symmetries. 16.4. Some simple examples. 16.5. Evading a no-go theorem

17. QCD at high temperature and density. 17.1. Simulating high temperature. 17.2. Introducing a chemical potential. 17.3. High quark mass limit and chiral limit. 17.4. Locating and characterizing the phase transition. 17.5. Simulating in a nearby ensemble. 17.6. Dimensional reduction and nonperturbative behavior. 17.7. Miscellaneous observables. 17.8. Nonzero density. 17.9. Spectral functions and maximum entropy.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 329-340) and index.

ISBN:

9786611919221

9781281919229

1281919225

9789812773982

9812773983

OCLC:

820942714