Lectures on Quantum Chromodynamics.
Title:
Lectures on Quantum Chromodynamics.
Author:
Smilga, Andrei.
ISBN:
9789812810595
Personal Author:
Physical Description:
1 online resource (352 pages)
Contents:
Contents -- Preface -- Notation and Conventions -- Introduction: Some History -- PART 1: FOUNDATIONS -- Lecture 1 Yang-Mills Field -- 1.1 Path Ordered Exponentials. Invariant Actions -- 1.2 Classical Solutions -- Lecture 2 Instantons -- 2.1 Topological Charge -- 2.2 Explicit Solutions -- Lecture 3 Path Integral in Quantum Mechanics -- 3.1 Conventional Approach -- 3.2 Euclidean Path Integral -- 3.3 Holomorphic Representation -- 3.4 Grassmann Dynamic Variables -- Lecture 4 Quantization of Gauge Theories -- 4.1 Dirac Quantization Procedure -- 4.2 Path Integral on the Lattice -- Lecture 5 θ-Vacuum -- 5.1 Quantum Pendulum -- 5.2 Large Gauge Transformations in Non-Abelian Theory -- PART 2: PERTURBATION THEORY -- Lecture 6 Diagram Technique in Simple and Complicated Theories -- 6.1 Feynman Rules from Path Integral -- 6.2 Fixing the Gauge -- Lecture 7 When the Gauge is Fixed... -- 7.1 Gribov Copies -- 7.2 Ward Identities -- 7.3 Ghosts and Unitarity -- 7.4 BRST Quantization -- Lecture 8 Regularization and Renormalization -- 8.1 Different Regularization Schemes -- 8.2 Renormalized Theory as an Effective Theory. Slavnov-Taylor Identities -- Lecture 9 Running Coupling Constant -- 9.1 One-loop Calculations -- 9.2 Renormalization Group. Asymptotic Freedom and Infrared Slavery -- 9.3 Observables. Ambiguities. Anomalous Dimensions -- Lecture 10 Weathering Infrared Storms -- 10.1 Bloch-Nordsieck Cancellation -- 10.2 Non-Abelian Complications. Coherent States -- Lecture 11 Collinear Singularities: Theory and Phenomenology -- 11.1 Double Logarithmic Asymptotics -- 11.2 Jet Cross Sections -- 11.3 DIS and KLN -- PART 3: NONPERTURBATIVE QCD -- Lecture 12 Symmetries: Anomalous and Not -- 12.1 Conformal Symmetry and its Breaking -- 12.2 Anomalous Chiral Symmetry.
12.3 Nonsinglet Chiral Symmetry and its Spontaneous Breaking. -- 12.4 Effective Chiral Langrangian -- Lecture 13 Quarks on Euclidean Lattice -- 13.1 Nielsen-Ninomiya's No-go Theorem -- 13.2 Ways to Go. The Ginsparg-Wilson Way. -- Lecture 14 Aspects of Chiral Symmetry -- 14.1 QCD Inequalities. Vafa-Witten Theorem -- 14.2 Euclidean Dirac Spectral Density. -- 14.3 Infrared Face of Anomaly -- 14.4 Chiral Symmetry Breaking and Confinement -- Lecture 15 Mesoscopic QCD -- 15.1 Partition Function: Nf = 1 -- 15.2 Partition Function: Nf ≥ 2 -- 15.3 Spectral Sum Rules -- 15.4 Instanton Gas and Instanton Liquid -- Lecture 16 Fairy QCD -- 16.1 Finite θ -- 16.2 Large Nc -- Lecture 17 ITEP Sum Rules: the Duality Festival -- 17.1 The Method -- 17.2 Nucleon Mass and Residue -- 17.3 Pion Formfactor and Nucleon Magnetic Moments -- Lecture 18 Hot and Dense QCD -- 18.1 Lukewarm Pion Gas. Restoration of Chiral Symmetry -- 18.2 Quark-Gluon Plasma -- 18.3 Finite Baryon Density. Color Superconductivity -- Lecture 19 Confinement -- 19.1 Weak Confinement and Strong Confinement. Wilson Criterium. -- 19.2 Schwinger Model -- 19.3 Polyakov Model -- 19.4 Dual Superconductivity -- Appendix Unitary groups -- Bibliography -- Index.
Abstract:
Quantum chromodynamics is the fundamental theory of strong interactions. It is a physical theory describing Nature. Lectures on Quantum Chromodynamics concentrates, however, not on the phenomenological aspect of QCD; books with comprehensive coverage of phenomenological issues have been written. What the reader will find in this book is a profound discussion on the theoretical foundations of QCD with emphasis on the nonperturbative formulation of the theory: What is gauge symmetry on the classical and on the quantum level? What is the path integral in field theory? How to define the path integral on the lattice, keeping intact as many symmetries of the continuum theory as possible? What is the QCD vacuum state? What is the effective low energy dynamics of QCD? How do the ITEP sum rules work? What happens if we heat and/or squeeze hadronic matter? Perturbative issues are also discussed: How to calculate Feynman graphs? What is the BRST symmetry? What is the meaning of the renormalization procedure? How to resum infrared and collinear singularities? And so on. The book is an outgrowth of the course of lectures given by the author for graduate students at ITEP in Moscow. Much extra material has been added. Sample Chapter(s). Introduction: Some History (331 KB). Lecture 1.1: Path Ordered Exponentials. Invariant Actions (624 KB). Lecture 1.2: Classical Solutions (266 KB). Lecture 2.1: Topological Charge (329 KB). Lecture 2.2: Explicit Solutions (338 KB). Lecture 3.1: Conventional Approach (330 KB). Lecture 3.2: Euclidean Path Integral (150 KB). Lecture 3.3: Holomorphic Representation (177 KB). Lecture 3.4: Grassmann Dynamic Variables (340 KB). Lecture 4.1: Dirac Quantization Procedure 782 KB). Lecture 4.2: Path Integral on the Lattice (330 KB). Lecture 5.1: Quantum Pendulum (534 KB). Lecture 5.2: Large Gauge Transformations in Non-Abelian Theory (395
KB). Contents: Foundations: Yang-Mills Field; Instantons; Path Integral in Quantum Mechanics; Quantization of Gauge Theories; Perturbation Theory: Diagram Technique in Simple and Complicated Theories; When the Gauge is Fixed … Regularization and Renormalization; Running Coupling Constant; Weathering Infrared Storms; Collinear Singularities: Theory and Phenomenology; Nonperturbative QCD: Symmetries: Anomalous and Not; Quarks on Euclidean Lattice; Aspects of Chiral Symmetry; Mesoscopic QCD; Fairy QCD; ITEP Sum Rules: The Duality Festival; Hot and Dense QCD; Confinement. Readership: High energy physicists and advanced level graduate students in high energy physics.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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