by Andrei Smilga (University of Nantes, France)

Preface (331k)
Table of Contents (145k)
Introduction: Some History (331k)
Lecture 1: Yang-Mills Field
Lecture 1.1: Path Ordered Exponentials. Invariant Actions (624k)
Lecture 1.2: Classical Solutions (266k)
Lecture 2: Instantons
Lecture 2.1: Topological Charge (329k)
Lecture 2.2: Explicit Solutions (338k)
Lecture 3: Path Integral in Quantum Mechanics
Lecture 3.1: Conventional Approach (330k)
Lecture 3.2: Euclidean Path Integral (150k)
Lecture 3.3: Holomorphic Representation (177k)
Lecture 3.4: Grassmann Dynamic Variables (340k)
Lecture 4: Quantization of Gauge Theories

Lecture 4.2: Path Integral on the Lattice (330k)
Lecture 5: Q-Vacuum
Lecture 5.1: Quantum Pendulum (534k)
Lecture 5.2: Large Gauge Transformations in Non-Abelian Theory (395k)

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.

• 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