Discrete Gauge Theory
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| Author | : Robert Oeckl |
| Publisher | : Imperial College Press |
| Total Pages | : 218 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 1860947379 |
This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork.
| Author | : D.G.B. Edelen |
| Publisher | : Elsevier |
| Total Pages | : 438 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0444600108 |
This new series Mechanics and Physics of Discrete Systems aims to provide a coherent picture of the modern development of discrete physical systems. Each volume will offer an orderly perspective of disciplines such as molecular dynamics, crystal mechanics and/or physics, dislocation, etc. Emphasized in particular are the fundamentals of mechanics and physics that play an essential role in engineering applications.Volume 1, Gauge Theory and Defects in Solids, presents a detailed development of a rational theory of the dynamics of defects and damage in solids. Solutions to field equations are used to determine stresses, dislocation densities and currents that arise from histories of loading of boundaries of bodies. Analysed in detail is a gauge theory with a gauge group that is not semi-simple, and whose action occurs at the classical macroscopic level. Yang-Mills theory is applied where the state variables are elastic displacements in solids, determination of mechanical and electromagnetic observables by choice of gauge conditions is demonstrated, and practices of classical dislocation theory are derived from first principles.
| Author | : Valery Rubakov |
| Publisher | : Princeton University Press |
| Total Pages | : 456 |
| Release | : 2009-02-09 |
| Genre | : Science |
| ISBN | : 1400825091 |
Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.
| Author | : Lochlainn O'Raifeartaigh |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2020-06-30 |
| Genre | : Science |
| ISBN | : 0691215111 |
During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase. O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrodinger, Klein, and London in the pre-war years, and by Pauli, Shaw, Yang-Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.
| Author | : Martin Ammon |
| Publisher | : Cambridge University Press |
| Total Pages | : 549 |
| Release | : 2015-04-09 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1107010349 |
The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.
| Author | : E. Brézin |
| Publisher | : Elsevier Science & Technology |
| Total Pages | : 678 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
Hardbound. This session of the Summer School in Theoretical Physics concentrated on the recent advances in areas of physics ranging from (super)strings to field theory and statistical mechanics. The articles contained in this volume provide a stimulating and up-to-date account of a rapidly growing subject.Discussion focussed on the many points of convergence between field theory and statistical mechanics: conformal field theory, field theory on a lattice, the study of strongly correlated electron systems, as in the Hubbard model, leading to topological Lagrangians, which are perhaps the key of the understanding of high Tc superconductivity or the fractional quantum Hall effect. The critical phenomena in (1+1) dimensions, in the domain in which quantum fluctuations are strong, are described for antiferromagnetic couplings by relativistic theories in which the methods of abelian or non-abelian bosonization are particularly powerful.
| Author | : Lars Brink |
| Publisher | : World Scientific |
| Total Pages | : 403 |
| Release | : 2016-11-01 |
| Genre | : Science |
| ISBN | : 9813144114 |
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics.All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics.
| Author | : John B. Kogut |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2003-12-24 |
| Genre | : Science |
| ISBN | : 1139441590 |
This book discusses the physical phases of quantum chromodynamics (QCD) in ordinary environments and also in extreme environments of high temperatures and high baryon number. It introduces lattice gauge theory, covering fundamentals and important developments, and emphasises the application of QCD to the study of matter in extreme environments.
| Author | : Amit Hagar |
| Publisher | : Cambridge University Press |
| Total Pages | : 281 |
| Release | : 2014-05 |
| Genre | : Science |
| ISBN | : 1107062802 |
Novel conceptual analysis, fresh historical perspectives, and concrete physical examples illuminate one of the most thought-provoking topics in physics.
| Author | : G. 't Hooft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 1468475711 |
Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.
