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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.
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.
This book introduces a number of topics in lattice gauge theories, including analytical as well as numerical computational methods and a discussion of modern developments in finite temperature QCD. It aims to provide young physicists with the necessary background and basic computational tools to understand the published literature and to carry out research on their own.
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.
"This book deals with new applications for coupled map lattices in quantum field theories and elementary particle physics"--P. xiii.
Few people studying Gauge Field Theory need to be convinced of the importance of the work of 't Hooft. This volume contains a selection of articles and review topics covering his well-known studies on the renormalization of non-Abelian gauge theorems, topological phenomena in gauge field theory and thoughts on the role of black holes in quantum gravity.The chapters are tied together by thoughtful commentaries which provide a background and the illumination of hindsight ? together they form a clear and coherent picture of the physical and theoretical importance of gauge theories and the gauge principle. This book is ideal for students and researchers.Gerard 't Hooft is Professor of Theoretical Physics at the University of Utrecht, The Netherlands. He has taught at Harvard, SLAC and Caltech prior to his present position. Other distinguished honors include being awarded the Dannie Heineman Prize, the Honorary Doctorate of Science from the University of Chicago, Wolf Prize of the State of Israel, Pius XI Medal (Vatican), and the Lorentz Medal (KNAW, Amsterdam).
This book contains a wide spectrum of articles which report the current research progress in topics concerning the dynamics of multiparticle production in high energy collision processes, with emphasis on nonperturbative aspects of QCD. The topics covered are: the phase diagram of QCD and related transitions; correlations and fluctuations in a variety of experiments involving multiparticle production (e+e- annihilation, pp collisions and heavy ion collisions); recent theoretical and experimental developments in interferometry and particle correlations; event-by-event fluctuations in high energy experiments; concepts of chaos and complexity in multiparticle dynamics and related phenomenology; relevant theoretical ideas based on QCD as a field theory.
Field theory, relying on the concept of continuous space and time while confronted with the quantum physical nature of observable quantities, still has some fundamental challenges to face. One such challenge is to understand the emergence of complexity in the behavior of interacting elementary fields, including among other things nontrivial phase structures of elementary matter at high energy density or an atypical emergence of statistical properties, e.g., when an apparent temperature is proportional to a constant acceleration in a homogeneous gravitational field. Most modern textbooks on thermal field theory are mainly concerned with how the field theory formalism should be used if a finite temperature is given. In contrast, this short primer explores how the phenomenon of temperature emerges physically for elementary fields - inquiring about the underlying kinetic field theory and the way energy fluctuations and other noise should be handled - and it investigates whether and how this harmonizes with traditional field theory concepts like spectral evolution, the Keldysh formalism, and phase transitions.
This is perhaps the most up-to-date book on Modern Elementary Particle Physics. The main content is an introduction to Yang-Mills fields, and the Standard Model of Particle Physics. A concise introduction to quarks is provided, with a discussion of the representations of SU(3).The Standard Model is presented in detail, including such topics as the Kobayashi-Maskawa matrix, chiral symmetry breaking, and the ?-vacuum. Theoretical topics of a more general nature include path integrals, topological solitons, renormalization group, effective potentials, the axial anomaly, and lattice gauge theory.This second edition, which has been expanded, incorporates the following new subjects: Wilson's renormalization scheme, and its relation to perturbative renormalization; pitfalls in quantizing gauge fields, such as the Gribov ambiguity; the lattice as a consistent regularization; Monte Carlo methods of solution; and the issues, folklores, and scenarios of quark confinement. More than a quarter of the book comprise of new materials.This book may be used as a text for a one-semester course on advanced quantum field theory, or reference book for particle physicists.
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.