Lectures on Quantum Chromodynamics

Quantum chromodynamics is the fundamental theory of strong interactions. It is a physical theory describing nature. This book 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. Preface......Page 8 Contents......Page 12 Notation and Conventions......Page 16 Introduction: Some History......Page 20 PART 1: FOUNDATIONS......Page 30 1.1 Path Ordered Exponentials. Invariant Actions......Page 32 1.2 Classical Solutions......Page 40 2.1 Topological Charge......Page 44 2.2 Explicit Solutions......Page 48 3.1 Conventional Approach......Page 54 3.2 Euclidean Path Integral......Page 59 3.3 Holomorphic Representation......Page 61 3.4 Grassmann Dynamic Variables......Page 63 4.1 Dirac Quantization Procedure......Page 68 4.2 Path Integral on the Lattice......Page 78 5.1 Quantum Pendulum......Page 84 5.2 Large Gauge Transformations in Non-Abelian Theory......Page 91 PART 2: PERTURBATION THEORY......Page 96 Lecture 6 Diagram Technique in Simple and Complicated Theories......Page 98 6.1 Feynman Rules from Path Integral......Page 99 6.2 Fixing the Gauge......Page 105 7.1 Gribov Copies......Page 114 7.2 Ward Identities......Page 117 7.3 Ghosts and Unitarity......Page 121 7.4 BRST Quantization......Page 125 8.1 Different Regularization Schemes......Page 132 8.2 Renormalized Theory as an Effective Theory. Slavnov-Taylor Identities......Page 138 9.1 One-loop Calculations......Page 148 9.2 Renormalization Group. Asymptotic Freedom and Infrared Slavery......Page 156 9.3 Observables. Ambiguities. Anomalous Dimensions......Page 162 Lecture 10 Weathering Infrared Storms......Page 172 10.1 Bloch-Nordsieck Cancellation......Page 173 10.2 Non-Abelian Complications. Coherent States......Page 180 11.1 Double Logarithmic Asymptotics......Page 186 11.2 Jet Cross Sections......Page 188 11.3 DIS and KLN......Page 194 PART 3: NONPERTURBATIVE QCD......Page 204 Lecture 12 Symmetries: Anomalous and Not......Page 206 12.1 Conformal Symmetry and its Breaking......Page 208 12.2 Anomalous Chiral Symmetry.......Page 213 12.3 Nonsinglet Chiral Symmetry and its Spontaneous Breaking.......Page 222 12.4 Effective Chiral Langrangian......Page 225 13.1 Nielsen-Ninomiya's No-go Theorem......Page 228 13.2 Ways to Go. The Ginsparg-Wilson Way.......Page 232 14.1 QCD Inequalities. Vafa-Witten Theorem......Page 240 14.2 Euclidean Dirac Spectral Density.......Page 243 14.3 Infrared Face of Anomaly......Page 248 14.4 Chiral Symmetry Breaking and Confinement......Page 252 15.1 Partition Function: Nf = 1......Page 256 15.2 Partition Function: Nf ≥ 2 ......Page 259 15.3 Spectral Sum Rules......Page 261 15.4 Instanton Gas and Instanton Liquid......Page 263 16.1 Finite θ......Page 270 16.2 Large Nc......Page 276 17.1 The Method......Page 284 17.2 Nucleon Mass and Residue......Page 286 17.3 Pion Formfactor and Nucleon Magnetic Moments......Page 297 Lecture 18 Hot and Dense QCD......Page 304 18.1 Lukewarm Pion Gas. Restoration of Chiral Symmetry......Page 306 18.2 Quark-Gluon Plasma......Page 311 18.3 Finite Baryon Density. Color Superconductivity......Page 316 Lecture 19 Confinement......Page 320 19.1 Weak Confinement and Strong Confinement. Wilson Criterium.......Page 321 19.2 Schwinger Model......Page 324 19.3 Polyakov Model......Page 327 19.4 Dual Superconductivity......Page 331 Appendix Unitary groups......Page 336 Bibliography......Page 344 Index......Page 348 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. 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