Lattice methods for quantum chromodynamics [[electronic resource] /] / Thomas DeGrand, Carleton DeTar

• Record Nr.: UNINA9910450958603321
• Autore: DeGrand T (Thomas)
• Pubbl/distr/stampa: Hackensack, NJ, : World Scientific, c2006
• ISBN: 1-281-91922-5; 9786611919221; 981-277-398-3
• Descrizione fisica: 1 online resource (xv, 345 p. ) : ill
• Altri autori (Persone): DeTarCarleton
• Disciplina: 539.7548
• Soggetti: Lattice gauge theories - Mathematical models; Quantum chromodynamics - Mathematical models; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (p. 329-340) and index.
• Nota di contenuto: 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.