Lectures On Quantum Chromodynamics

By: Andrei Smilga

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Hardcover | 29 November 2001

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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.

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Preface	p. vii
Notation and Conventions	p. xv
Introduction: Some History	p. xix
Foundations
Yang-Mills Field	p. 3
Path Ordered Exponentials. Invariant Actions	p. 3
Classical Solutions	p. 11
Instantons	p. 15
Topological Charge	p. 15
Explicit Solutions	p. 19
Path Integral in Quantum Mechanics	p. 25
Conventional Approach	p. 25
Euclidean Path Integral	p. 30
Holomorphic Representation	p. 32
Grassmann Dynamic Variables	p. 34
Quantization of Gauge Theories	p. 39
Dirac Quantization Procedure	p. 39
Path Integral on the Lattice	p. 49
[theta]-Vacuum	p. 55
Quantum Pendulum	p. 55
Large Gauge Transformations in Non-Abelian Theory	p. 62
Perturbation Theory
Diagram Technique in Simple and Complicated Theories	p. 69
Feynman Rules from Path Integral	p. 70
Fixing the Gauge	p. 76
When the Gauge is Fixed ...	p. 85
Gribov Copies	p. 85
Ward Identities	p. 88
Ghosts and Unitarity	p. 92
BRST Quantization	p. 96
Regularization and Renormalization	p. 103
Different Regularization Schemes	p. 103
Renormalized Theory as an Effective Theory. Slavnov-Taylor Identities	p. 109
Running Coupling Constant	p. 119
One-loop Calculations	p. 119
Renormalization Group. Asymptotic Freedom and Infrared Slavery	p. 127
Observables. Ambiguities. Anomalous Dimensions	p. 133
Weathering Infrared Storms	p. 143
Bloch-Nordsieck Cancellation	p. 144
Non-Abelian Complications. Coherent States	p. 151
Collinear Singularities: Theory and Phenomenology	p. 157
Double Logarithmic Asymptotics	p. 157
Jet Cross Sections	p. 159
DIS and KLN	p. 165
Nonperturbative QCD
Symmetries: Anomalous and Not	p. 177
Conformal Symmetry and its Breaking	p. 179
Anomalous Chiral Symmetry	p. 184
Nonsinglet Chiral Symmetry and its Spontaneous Breaking	p. 193
Effective Chiral Langrangian	p. 196
Quarks on Euclidean Lattice	p. 199
Nielsen-Ninomiya's No-go Theorem	p. 199
Ways to Go. The Ginsparg-Wilson Way	p. 203
Aspects of Chiral Symmetry	p. 211
QCD Inequalities. Vafa-Witten Theorem	p. 211
Euclidean Dirac Spectral Density	p. 214
Infrared Face of Anomaly	p. 219
Chiral Symmetry Breaking and Confinement	p. 223
Mesoscopic QCD	p. 227
Partition Function: N[subscript f] = 1	p. 227
Partition Function: N[subscript f] [greater than or equal] 2	p. 230
Spectral Sum Rules	p. 232
Instanton Gas and Instanton Liquid	p. 234
Fairy QCD	p. 241
Finite [theta]	p. 241
Large N[subscript c]	p. 247
ITEP Sum Rules: the Duality Festival	p. 255
The Method	p. 255
Nucleon Mass and Residue	p. 257
Pion Formfactor and Nucleon Magnetic Moments	p. 268
Hot and Dense QCD	p. 275
Lukewarm Pion Gas. Restoration of Chiral Symmetry	p. 277
Quark-Gluon Plasma	p. 282
Finite Baryon Density. Color Superconductivity	p. 287
Confinement	p. 291
Weak Confinement and Strong Confinement. Wilson Criterium	p. 292
Schwinger Model	p. 295
Polyakov Model	p. 298
Dual Superconductivity	p. 302
Unitary groups	p. 307
Bibliography	p. 315
Index	p. 319
Table of Contents provided by Syndetics. All Rights Reserved.

Lectures On Quantum Chromodynamics

At a Glance

Hardcover

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