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1 online resource (320 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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Intro -- CONTENTS -- Preface -- Fixed Point Actions, Symmetries and Symmetry Transformations on the Lattice P. Hasenfratz -- 1. Introduction -- 2. Cut-off effects: a numerical experiment on the running coupling -- 3. Renormalization group and the fixed point action -- 4. Saddle point equation for the fixed point action i n QCD -- 5. Perfect classical lattice theories -- 6. The FP Dirac operator satisfies the Ginsparg-Wilson relation -- 7. Lattice regularization and symmetry transformations -- Acknowledgements -- References -- Algorithms for Dynamical Fennions A. D. Kennedy -- 1. Introduction -- 2. Building Blocks for Monte Carlo Methods -- 2.1. Monte Carlo Methods -- 2.2. Central Limit Theorem -- 2.3. Markov Chains -- 2.4. Convergence of Markov Chains -- 2.5. Detailed Balance and the Metropolis Algorithm -- 2.6. Composition of Markov Steps -- 2.7. Coupling from the Past -- 2.8. Autocorrelations -- 2.8.1. Exponential Autocorrelation -- 2.8.2. Integrated Autocorrelation -- 2.9. Hybrid Monte Carlo -- 2.10. MDMC -- 2.11. Partial Momentum Refreshment -- 2.12. Baker-Campbell-Hausdorff (B CH) formula -- 2.13. Symplectic Integrators -- 2.13.1. Integrator Instability -- 2.14. Multiple Timescales -- 2.15. Dynamical Fewnions -- 2.16. Reversibility -- 3. The RHMC Algorithm -- 3.1. Polynomial Approximation -- 3.2. Chebyshev's theorem -- 3.3. Chebyshev Polynomials -- 3.4. Chebyshev Optimal Rational Approximation -- 3.5. Non-Linearity of CG Solver -- 3.6. Rational Matrix Approximation -- 3.7. 'No Free Lunch' Theorem -- 3.8. Multiple Pseudofermions -- 3.8.1. The Hasenbusch Method -- 3.9. Violation of NFL theorem -- 3.10. Rational Hybrid Monte Carlo -- 3.11. Comparison with R Algorithm -- 3.11.1. Finite Temperature QCD -- 3.11.2. 2+1 Domain Wall Fermions -- 3.12. Multiple Pseudofermions with Multiple Timescales -- 3.13. Lz versus I -- , Force Norms |
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3.14. Berlin Wall for Wilson fermions -- 3.15. Conclusions (RHMC) -- 4. 5D Algorithms for Chiral Lattice Fermions -- 4.1. On-shell chiral symmetry -- 4.2. Neuberger's Operator -- 4.3. 5D Chiral Fermions -- 4.4. Choice of Kernel -- 4.5. Schur Complement -- 4.6. Constraint -- 4.7. Approximation -- 4.7.1. Hyperbolic Tangent -- 4.7.2. Zolotarev's Formula -- 4.7.3. Errors -- 4.8. Representation -- 4.8.1. Continued Fraction -- 4.8.2. Partial Fraction -- 4.8.3. Euclidean Cayley Transform -- 4.8.4. Relation to Domain Wall Fermions -- 4.9. Chiral Symmetry Breaking -- 4.10. Numerical Studies -- 4.11. Future Work -- Acknowledgments -- References -- Applications of Chiral Perturbation Theory to Lattice QCD Stephen R. Sharpe -- 1. Overview and Aims -- 2. Review of xPT in the continuum -- 2.1. Eflective Field Theories in general -- 2 . 2 . Chiral symmetry in QCD and its breaking -- 2.3. Constructing the pionic effective Lagrangian2' -- 2.3.1. Building blocks for C e -- 2.3.2. Brief aside on vacuum structure -- 2.3.3. Properties of pseudo-Nambu-Goldstone bosons at leading order -- 2.3.4. Lessons for lattice simulations -- 2.3.5. Power counting an XPT (M = 0) -- 2.3.6. Lessons for lattice simulations (continued) -- 2.3.7. Technical aside: adding sources -- 2.3.8. Final form of chiral Lagrangian -- 2.4. Examples of NLO results -- 2.4.1. Lessons for lattice simulations (continued) -- 2.4.2. Volume dependence from XPT -- 2.4.3. Convergence of XPT -- 2.4.4. Extension to "heavy" particles -- 3. Incorporating discretization errors into X P T -- 3.1. Why incorporate discretization errors? -- 3.2. General strategy -- 3.3. Application to Wilson & twisted mass fermions -- 3.4. Determining the local effective Lagrangian -- 3.5. Symanzik effective action for tmLQCD -- 3.6. Mapping the Symanzik action into XPT -- 3.6.1. Power counting and terminology |
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3.6.2. Mapping Lio and Lgio into XPT -- 3.7. Results for m, N an&, (GSM regime) -- 3.7.1. TmXPT at LO -- 3.7.2. tmXPT at NLO -- 3.8. Defining m, and the twist angle -- 3.9. Results for m, N a2A& (Aoki regime) -- 3.9.1. Applications to lattice simulations -- 3.9.2. Bending near maximal twist -- 3.9.3. Does tmLQCD work in practice? -- 4. Partial quenching and PQXPT -- 4.1. What is PQQCD and why is it useful? -- 4.2. A field theoretic formulation of PQQCD -- 4.3. Developing PQXPT -- 4.3.1. Symmetries of PQQCD -- 4.3.2. Brief primer on graded Lie groups -- 4.3.3. Chiral symmetry breaking -- 4.3.4. Constructing the EFT -- 4.3.5. What about C pQ ? -- 4.4. PQXPT at LO -- 4.5. NLO calculations in PQXPT and outlook -- 4.5.1. Status of PQXPT calculations -- 4.5.2. A final example: L7 -- Acknowledgments -- References -- Lattice QCD with a Chiral Twist S. Sint -- 1. Introduction -- 2. Continuum QCD and chiral transformations -- 3. Standard Wilson quarks -- 3.1. Wilson quarks and unphysical fernionic zero modes -- 3.1.1. Quenched and partially quenched approximations -- 3.1.2. Potential problems in the Hybrid Monte Carlo algorithm -- 4. Twisted mass lattice QCD -- 4.1. Equivalence between tmQCD and QCD -- 4.2. Beyond the formal continuum theory -- 4.3. Lattice tmQCD with Wilson quarks -- 5. A few applications of tmQCD -- 5.1. Computation of F, -- 5.2. Direct determination of the chiral condensate -- 5.3. The computation of BK -- 5.3.1. Renorrnalisation of OVA+A -- 5.3.2. Results for BK in the quenched approximation -- 5.4. Further applications -- 6. O(a) improvement and tmQCD -- 6.1. O(a) improvement of Wilson quarks -- 6.2. Automatic O(a) improvement of tmQCD in a finite volume -- 6.2.1. Uncertainty of the chiral limit -- 6.3. Automatic O(a) improvement in infinite volume -- 7. Consequences of Parity and Flavour breaking |
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7.1. Non-degenerate quarks and additional flavours -- 8. A chiral twist to the QCD Schrodinger functional -- 8.1. The QCD Schrodinger functional -- 8.2. Decoupling of heavy quarks in SF schemes -- 8.2.1. Free quarks with SF boundary conditions -- 8.3. SF boundary conditions and chiral rotations -- 8.4. SF schemes with Wilson quarks and O(a) improvement -- 8.5. The Schrodinger functional and O(a) improvement -- 8.6. The SF with chirally rotated boundary conditions -- 8.6.1. Symmetries and Counterterms -- 8.7. An example from perturbation theory -- 9. Conclusions -- Acknowledgments -- References -- Non-Perturbative QCD: Renormalization, O(A) - Improvement and Matching to Heavy Quark Effective Theory Rainer Sommer -- 1. Introduction -- 1.1. Basic renormalization: hadron spectrum -- 1.2. Scale dependent renormalization and fundamental parameters of QCD -- 1.3. Irrelevant operators -- 1.4. Heavy Quark Effective Theory -- Lecture I. The Schrodinger functional and O(a)-improvement of lattice QCD -- 1.1. The Schrodinger functional (SF) -- 1.1.1. Definition -- 1.1.2. Quantum mechanical interpretation -- 1.1.3. Background field -- 1.1.4. Perturbative expansion -- 1.1.5. General renormalization properties -- 1.1.6. Renormalized coupling -- 1.1.7. Quarks -- 1.1.7.1. Correlation functions -- 1.1.7.2. Renormalized mass -- 1.1.8. Lattice formulation -- 1.1.8.1. Boundary conditions and the background field -- 1.1.8.2. Lattice artifacts -- 1.1.8.3. Explicit expression for -- 1.1.9. More literature -- 1.2. Chiral symmetry and O(a)-improvement -- 1.2.1. Chiml Ward identities -- 1.2.2. On-shell O(a)-improvement -- 1.2.2.1. Motivation -- 1.2.2.2. A warning from two dimensions -- 1.2.2.3. Symanzik's local eflective theory (SET) -- 1.2.2.4. Improved lattice action and fields -- 1.2.3. The PCAC relation -- 1.2.4. Non-perturbative improvement |
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1.2.4.1. The constant physics condition -- 1.2.4.2. Summary of results -- 1.2.4.3. O(a2) effects after improvement for Nf = 2 -- 1.2.4.4. Do we need more? -- Lecture 11. Fundamental parameters of QCD from the lattice -- 11.1. The problem of scale dependent renormalization -- 11.1.1. The extraction of (Y f r o m experiments -- 11.1.2. Reaching large scales in lattice QCD -- 11.2. The computation of a ( p ) and A -- 11.2.1. The step scaling function -- 11.2.2. Lattice spacing eflects in perturbation theory -- 11.2.3. The continuum limit - universality -- 11.2.4. The running of the coupling -- 11.2.5. The A parameter -- 11.2.6. Discussion -- 11.2.7. Improvements are necessary -- 11.3. Renormalization group invariant quark masses -- 11.4. Renormalization scale dependence of other composite operators -- Lecture 111. Non-perturbative Heavy Quark Effective Theory -- 111.1. Introduction -- 111.1.1. Derivation of the classical theory -- 111.2. The effective quantum field theory -- 111.2.1. The static approximation and its symmetries -- 111.2.1.1. Lattice formulation -- 111.2.1.2. Renormalization -- 111.2.2. Including l/mb corrections -- 111.2.2.1. limb-expansion of correlation functions and matrix elements -- 111.2.2.2. Renormalization and continuum limit -- 111.2.2.3. The flavor currents in the effective theory -- 111.2.3. Schrodinger functional correlation functions -- 111.3. The scope of the theory -- 111.3.1. A first example: the decay constant -- 111.3.1.1. Renormalization and matching in perturbation theory -- 111.3.1.2. Beyond the leading order: the need for non-perturbative conversion functions -- 111.3.1.3. Splitting leading order (LO) and next to leading order (NL 0) -- 111.3.2. A second example: mass formulae -- 111.4. Non-perturbative tests of HQET -- 111.5. Strategy for non-perturbative matching -- 111.5.1. Matching in small volume |
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111.5.2. Step scaling functions |
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This book consists of a series of lectures to cover every facet of the modern version of lattice QCD. All the lectures are self-contained starting with the necessary background material and ending up with the latest development. Most of the lectures are given by pioneers in the field. This book may be useful as an advanced textbook for graduate students in particle physics and its modern and fascinating contents will inspire the interest of the non-experts. Sample Chapter(s). Chapter 1: Fixed Point Actions, Symmetries and Symmetry Transformations on the Lattice (523 KB). Contents: Fixed Point Actions, Symmetries and Symmetry Transformations on the Lattice (P Hasenfratz); Algorithms for Dynamical Fermions (A D Kennedy); Applications of Chiral Perturbation Theory to Lattice QCD (S R Sharpe); Lattice QCD with a Chiral Twist (S Sint); NonPerturbative QCD: Renormalization, O(A)Improvement and Matching to Heavy Quark Effective Theory (R Sommer). Readership: Graduate students in particle physics; non-experts interested in lattice gauge theories |
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Description based on publisher supplied metadata and other sources |
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
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Print version: Kuramashi, Yoshinobu Perspectives In Lattice Qcd - Proceedings Of The Workshop : Proceedings of the Workshop
Singapore : World Scientific Publishing Company,c2007 9789812700001
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| Subject |
Quantum chromodynamics -- Congresses.;Lattice field theory -- Congresses.;Lattice gauge theories -- Congresses
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Electronic books
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