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.

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

"I recommend it for all graduate students in physics. The book has a number of worked examples in the tradition of Landau and Lifshifts."

"It is nicely illustrated in a clear and pedagogical manner. The author was an important contributor in many issues reflected in the book. This makes his presentation scientifically solid on the one hand, and vivid on the other ... I found this text to be the only one on the market which I could recommend to my students in the QCD class. It can (and hopefully will) serve as a prototype for the future comprehensive course book which will parallel the famous course of theoretical physics by Landau and Lifshitz."

"Quantum chromodynamics is one of the cornerstones of our understanding of the basic laws of nature, perhaps even the most beautiful one of these. It is important that our physics students are given the opportunity to familiarize themselves with it. The book of Andrei Smilga offers an excellent introduction, as it explains the essential elements of QCD in detail, from several different vantage points. The emphasis is on the principles that underlie our present understanding. I strongly recommend this book, which contains an original and comprehensive discussion of the key concepts."

"The most impressive is the third part of the book where the author discusses nonperturbative phenomena including anomalies, Goldstone bosons, lattice, confinement. The language of the book is very colorful which helps in explanation of quite complicated notions ... In summary, I think that the book makes a rather unique source for a deep study of the field, both for newcomers like graduate students and for established researchers."

“The intended audience ranges from graduate students to scientific researchers in the field; hence, the volume represents a beneficial investment for both individuals and libraries.”