Group Structure Of Gauge Theories

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Group Structure Of Gauge Theories

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Author : L. O'Raifeartaigh
language : en
Publisher: Cambridge University Press
Release Date : 1986

Group Structure Of Gauge Theories written by L. O'Raifeartaigh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.

The first portion of the text is devoted to a review of those aspects of Lie groups necessary for the application of group theory to the physics of particles and fields. The second describes the way in which compact Lie groups are used to construct gauge theories.

The Dawning Of Gauge Theory

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Author : Lochlainn O'Raifeartaigh
language : en
Publisher: Princeton University Press
Release Date : 2020-06-30

The Dawning Of Gauge Theory written by Lochlainn O'Raifeartaigh and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-30 with Science categories.

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.

Discrete Gauge Theory

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Author : Robert Oeckl
language : en
Publisher: Imperial College Press
Release Date : 2005

Discrete Gauge Theory written by Robert Oeckl and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

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.

Mathematical Gauge Theory

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Author : Mark J.D. Hamilton
language : en
Publisher: Springer
Release Date : 2017-12-06

Mathematical Gauge Theory written by Mark J.D. Hamilton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-06 with Mathematics categories.

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.

Gauge Theories Of Gravitation

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Author : Friedrich W. Hehl
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2013

Gauge Theories Of Gravitation written by Friedrich W. Hehl and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.

Foreword by T W B Kibble, FRSIn the last five decades, the gauge approach to gravity has represented a research area of increasing importance for our understanding of the physics of fundamental interactions. A full clarification of the gauge dynamics of gravity is expected to be the last missing link to the hidden structure of a consistent unification of all the fundamental interactions, based on the gauge principle. The aim of the present reprint volume, with commentaries by Milutin Blagojević and Friedrich W Hehl, is to introduce graduate and advanced undergraduate students of theoretical or mathematical physics, or any other interested researcher, to the field of classical gauge theories of gravity.This is not just an ordinary reprint volume; it is a guide to the literature on gauge theories of gravity. The reader is encouraged first to study the introductory commentaries and to become familiar with the basic content of the reprints and related ideas, then he/she can choose to read a specific reprint or reprints, and after that he/she should return again to the text and explore the additional literature, etc. The interaction is intended to be more complex than just starting with commentaries and ending with reprints.

Gauge Theories In The Twentieth Century

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Author : John C. Taylor
language : en
Publisher: World Scientific
Release Date : 2001

Gauge Theories In The Twentieth Century written by John C. Taylor and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.

By the end of the 1970s, it was clear that all the known forces of nature (including, in a sense, gravity) were examples of gauge theories, characterized by invariance under symmetry transformations chosen independently at each position and each time. These ideas culminated with the finding of the W and Z gauge bosons (and perhaps also the Higgs boson). This important book brings together the key papers in the history of gauge theories, including the discoveries of: the role of gauge transformations in the quantum theory of electrically charged particles in the 1920s; nonabelian gauge groups in the 1950s; vacuum symmetry-breaking in the 1960s; asymptotic freedom in the 1970s. A short introduction explains the significance of the papers, and the connections between them. Contents: Gauge Invariance in Electromagnetism; Non-Abelian Gauge Theories; Gravity as a Gauge Theory; Gauge Invariance and Superconductivity; Spontaneous Symmetry Breaking and Particle Physics; Gauge-Fixing in Non-Abelian Gauge Theories; Gauge Identities and Unitarity; Asymptotic Freedom; Monopoles and Vortex Lines; Non-Pertubative Approaches; Instantons and Vacuum Structure; Three-Dimensional Gauge Fields and Topological Actions; Gauge Theories and Mathematics. Readership: Graduate students, researchers and lecturers in mathematical, theoretical, quantum and high energy physics, as well as historians of science.

Group Structure Of Gauge Theories

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Author : Lochlainn O'Raifeartaigh
language : en
Publisher:
Release Date : 1986

Group Structure Of Gauge Theories written by Lochlainn O'Raifeartaigh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.

This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.

Differential Geometry Gauge Theories And Gravity

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Author : M. Göckeler
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-28

Differential Geometry Gauge Theories And Gravity written by M. Göckeler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-28 with Mathematics categories.

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Classical Theory Of Gauge Fields

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Author : Valery Rubakov
language : en
Publisher: Princeton University Press
Release Date : 2009-02-09

Classical Theory Of Gauge Fields written by Valery Rubakov and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Science categories.

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.