This book introduces a rapidly growing new research area — the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behavior of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our Universe shortly after the Big Bang. In particular, chaos is rediscovered in a new appearance in these studies: in gauge theories the well-known divergence of initially adjacent phase space trajectories leads over into a quasi-thermal distribution of energy with a saturated average distance of different field configurations. This particular behavior is due to the compactness of the gauge group. Generally this book is divided into two main parts: the first part mainly deals with the “classical” discovery of chaos in gauge field theory while the second part presents methods and research achievements in recent years. One chapter is devoted entirely to the presentation and discussion of computational problems. The major theme, returning again and again throughout the book, is of course the phenomenon with a thousand faces — chaos itself. This book is intended to be a research book which introduces the reader to a new research field, presenting the basic new ideas in detail but just briefly touching on the problems of other related fields, like perturbative or lattice gauge theory, or dissipative chaos. The terminology of these related fields are, however, used. Exercises are also included in this book. They deepen the reader's understanding of special issues and at the same time offer more information on related problems. For the convenience of the fast reader, solutions are presented right after the problems. Contents:IntroductionChaotic DynamicsChaos in Gauge TheoryTopological Field TheoriesLattice Gauge TheoryHamiltonian Lattice Gauge TheoryComputing SU(2) Gauge TheoryChaos in Lattice Gauge TheoryApplications and ExtensionsBeyond the Classical TheoryChaos and Confinement Readership: Nonlinear scientists, high energy physicists, mathematicians and engineers. keywords:Non-Abelian Gauge Fields;Periodic Orbits;Lyapunov Exponents;Classical and Quantum YangâMills Mechanics;Higgs Mechanism;Self-Thermalization via Chaos;Chaos and Confinement;Quark-Gluon Plasma;Lattice Gauge Theory;Monte Carlo Methods;Physics;Field Theory;Chaos;Gauge;Lattice;Thermalization;Entropy;Computing “This book is a good place to approach the research area of chaos applied to gauge field theories.” Mathematical Reviews

## Lattice Gauge Theories

*An Introduction*

## Correlations & Fluctuations in QCD

*Proceedings of the 10th International Workshop on Multiparticle Production, Crete, Greece, 8-15 June 2002*

## Introduction to Path-integral Methods in Physics and Polymer Science

This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.

## Quantum Chromodynamics: Collisions, Confinement And Chaos - Proceedings Of The Workshop

During the week of 3-8 June 1996, approximately 83 theoretical (and 2 experimental) physicists interested in the current problems of Quantum Chromodynamics (QCD) gathered at the American University of Paris, France, to present and discuss a total of 59 papers on Collisions, Confinement, and Chaos in QCD. Each of these three subfields filled at least two half-day sessions; and another four half-day sessions were devoted to miscellaneous and interesting papers on Quantum Field Theory (QFT), and especially on the proper construction of high-energy scattering amplitudes.

## Theory of Spin Lattices and Lattice Gauge Models

*Proceedings of the 165th WE-Heraeus-Seminar Held at Physikzentrum Bad Honnef, Germany, 14–16 October 1996*

## Elementary Symbolic Dynamics and Chaos in Dissipative Systems

This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators.

## Classical and Quantum Electrodynamics and the B(3) Field

It is well known that classical electrodynamics is riddled with internal inconsistencies springing from the fact that it is a linear, Abelian theory in which the potentials are unphysical. This volume offers a self-consistent hypothesis which removes some of these problems, as well as builds a framework on which linear and nonlinear optics are treated as a non-Abelian gauge field theory based on the emergence of the fundamental magnetizing field of radiation, the B(3) field. Contents: Interaction of Electromagnetic Radiation with One Fermion; The Field Equations of Classical O (3) b Electrodynamics; Origin of Electrodynamics in the General Theory of Gauge Fields; Nonlinear Propagation in O (3) b Electrodynamics: Solitons and Instantons; Physical Phase Effects in O (3) b Electrodynamics; Quantum Electrodynamics and the B (3) Field; Quantum Chaos, Topological Indices and Gauge Theories; Field Theory of O (3) b QED and Unification with Weak and Nuclear Interactions; Potential Applications of O (3) b QED; Duality and Fundamental Problems. Readership: Graduate and undergraduates in physics (electromagnetism), differential geometry & topology, electrical & electronic engineering, theoretical & physical chemistry, chaos and dynamical systems.

## Geometric Structures of Phase Space in Multi-Dimensional Chaos

*Applications to Chemical Reaction Dynamics in Complex Systems*

## Nonperturbative Quantum-field-theoretic Methods and Their Applications

*Proceedings of the 24th Johns Hopkins Workshop, Bolyai College, Budapest, Hungary, 19-21 August 2000*