Among the several distinct ways of formulating and quantizing a Hamiltonian system, the light cone approach enjoys special status because it has the largest stability group. The aim of this volume is to present recent achievements and open problems in this rather unusual quantization framework to a large audience. The formulation is set up in a comprehensive introduction where the issues are also clearly indicated with specific examples: vacuum structure, signature of non-perturbative effects, chiral symmetry breaking, light cone gauge theories, etc. The following chapters address these topics through a selection of the most relevant contributions presented at Les Houches. This volume should prove valuable to newcomers in the field, and graduates and academics.

A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.

This 2004 book provides a pedagogical introduction to the perturbative and non-perturbative aspects of quantum chromodynamics (QCD). The text introduces the basic theory of QCD and its historical development, covering pre-QCD ideas of strong interactions such as the quark and parton models, the notion of colours and the S-matrix approach. The author then discusses gauge theory, techniques of dimensional regularization and renormalization, deep inelastic scattering and hard processes in hadron collisions, hadron jets and e+e- annihilations. Other topics include power corrections and the technologies of the Shifman-Vainshtein-Zakharov operating product expansion. The final parts of the book are devoted to modern non-perturbative approaches to QCD and the phenomenological aspects of QCD spectral sum rules. The book will be a valuable reference for graduate students and researchers in high-energy particle and nuclear physics, both theoretical and experimental. This book has been reissued as an Open Access publication on Cambridge Core.

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.

This volume presents the important recent progress in both theoretical and phenomenological issues of strong coupling gauge theories, with/without supersymmetry and extra dimensions, etc. Emphasis is placed on dynamical symmetry breaking with large anomalous dimensions governed by the dynamics near the nontrivial fixed point. Also presented are recent developments of the corresponding effective field theories, such as those including light spectra other than the NambuOCoGoldstone particles. This book is a must for all those who are interested in dynamical symmetry breaking and effective field theories in a modern version. Contents: Light-Front Quantization of Gauge Theories (S J Brodsky); Significance of the Renormalization Constant of the Color Gauge Field (K Nishijima & M Chaichian); Mass Gap and Color Confinement in YangOCoMills Theory Based on Asymptotic Solutions of SD Equation (K-I Kondo); Strong Coupling Approach to Transverse Lattice QCD (S Dalley); Vector Manifestation of Chiral Symmetry (M Harada); Locking Internal and Space-Symmetries: Relativistic Vector Condensation (F Sannino); A Practical Gauge Invariant Construction of Abelian Chiral Gauge Theories on the Lattice (Y Kikukawa); Neutrino Masses in Theories with Dynamical Breaking of Electroweak and Extended Gauge Symmetries (T Appelquist & R Schrock); Dynamical Electroweak Symmetry Breaking from Extra Dimensions (M Hashimoto et al.); Classical Solutions of Field Equations in Randall Sundrum Brane Worlds (D Karasik et al.); Flavor Constraints on Theory Space (E H Simmons et al.); Neutrino Mass Matrix in Terms of Up-Quark Masses (M Bando & M Obara); and other papers. Readership: Graduate students and researchers in high energy physics, particularly those interested in dynamical symmetry breaking and effective field theories."

Particle production is an important topic in nuclear and particle physics. At high energies, particle production is considered to proceed via parton branching and subsequent fragmentation into hadrons. The study of the dynamics of this process and the study of the structure of hadrons in the context of quantum chromodynamics (QCD) belong to the challenges of the standard model of elementary particle physics, requiring new, nonperturba tive approaches in field theory. Within a nucleus, many-body dynamics is important and particle production may be used to determine many features of a non-equilibrium quantum system at low or high temperatures. At this Advanced Study Institute the different aspects of particle pro duction were expanded upon in a series of lectures given by experts in their fields, covering topics ranging from near-threshold meson production in proton-proton collisions to correlations in multi-GeV jet fragmentation in high-energy scattering processes and signals of a quark-gluon plasma formed in ultra-relativistic heavy-ion collisions. Strong emphasis was placed not only on state of the art research, but also on the necessary physics back ground. The lectures were supplemented by problem sets and discussion sessions. There was also time for students to present short contributions on their research.