Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

Proceedings of a NATO ASI and Isaac Newton Institute Workshop held in Cambridge, UK, June 23-July 4, 1997

This book consists of reviews covering all aspects of quantum chromodynamics as we know it today. The articles have been written by recognized experts in this field, in honor of the 75th birthday of Professor Boris Ioffe. Combining features of a handbook and a textbook, this is the most comprehensive source of information on the present status of QCD. It is intended for students as well as physicists — both theorists and experimentalists.Each review is self-contained and pedagogically structured, providing the general formulation of the problem, telling where it stands with respect to other issues and why it is interesting and important, presenting the history of the subject, qualitative insights, and so on. The first part of the book is historical in nature. It includes, among other articles, Boris Ioffe's and Yuri Orlov's memoirs on high energy physics in the 1950's, a note by B V Geshkenbein on Ioffe's career in particle physics, and an essay on the discovery of asymptotic freedom written by David Gross.

Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004

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: YangOCoMills 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 OC 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."

This book contains articles on the latest research in QCD from some of the leading experts in the field. These are based on talks presented at the Continuous Advances in QCD 2004 workshop held at the William I Fine Theoretical Physics Institute.The book will be a useful reference source for graduate students and researchers in high energy physics.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

This volume summarizes our contemporary understanding of the deconfinement transition in QCD at finite temperature and chemical potential. Questions as to whether a quark-gluon plasma exists in the interior of dense astrophysical objects or which bound-state signals have to be studied in order to unambiguously detect the QCD phase transition(s) in future heavy-ion collision programmes at RHIC and LHC are addressed. Progress in answering these questions requires a fusion of lattice QCD with other nonperturbative approaches and low-energy effective models for QCD. Experts in these fields present in the book their methods and their results in understanding the deconfinement phenomenon.