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Mathematical Gauge Theory
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Book Synopsis Mathematical Gauge Theory by : Mark J.D. Hamilton
Download or read book Mathematical Gauge Theory written by Mark J.D. Hamilton and published by Springer. This book was released on 2017-12-06 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Gauge Theory by : Mark J.D. Hamilton
Download or read book Mathematical Gauge Theory written by Mark J.D. Hamilton and published by Springer. This book was released on 2018-01-10 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Gauge Theory and Variational Principles by : David Bleecker
Download or read book Gauge Theory and Variational Principles written by David Bleecker and published by Courier Corporation. This book was released on 2013-01-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.
Book Synopsis Group Structure of Gauge Theories by : L. O'Raifeartaigh
Download or read book Group Structure of Gauge Theories written by L. O'Raifeartaigh and published by Cambridge University Press. This book was released on 1986 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Methods of Contemporary Gauge Theory by : Yuri Makeenko
Download or read book Methods of Contemporary Gauge Theory written by Yuri Makeenko and published by Cambridge University Press. This book was released on 2023-07-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry, Gauge Theories, and Gravity by : M. Göckeler
Download or read book Differential Geometry, Gauge Theories, and Gravity written by M. Göckeler and published by Cambridge University Press. This book was released on 1989-07-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modern Differential Geometry in Gauge Theories by : Anastasios Mallios
Download or read book Modern Differential Geometry in Gauge Theories written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Book Synopsis The Mathematical Foundations of Gauge Theories by : Kishore B. Marathe
Download or read book The Mathematical Foundations of Gauge Theories written by Kishore B. Marathe and published by North Holland. This book was released on 1992 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.
Book Synopsis Gauging What's Real by : Richard Healey
Download or read book Gauging What's Real written by Richard Healey and published by Oxford University Press on Demand. This book was released on 2007-09-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge theories have provided our most successful representations of the fundamental forces of nature. But how do such representations work? Healey aims to answer this question, and defends a distinctive thesis which proves that loops rather than points are the locations of fundamental properties.
Book Synopsis Lattice Gauge Theories: An Introduction by : Heinz J Rothe
Download or read book Lattice Gauge Theories: An Introduction written by Heinz J Rothe and published by World Scientific. This book was released on 1992-01-29 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.
Book Synopsis An Elementary Primer for Gauge Theory by : K. Moriyasu
Download or read book An Elementary Primer for Gauge Theory written by K. Moriyasu and published by World Scientific. This book was released on 1983 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge theory is now recognized as one of the most revolutionary discoveries in physics since the development of quantum mechanics. This primer explains how and why gauge theory has dramatically changed our view of the fundamental forces of nature. The text is designed for the non-specialist. A new, intuitive approach is used to make the ideas of gauge theory accessible to both scientists and students with only a background in quantum mechanics. Emphasis is placed on the physics rather than the formalism.
Book Synopsis Chern-Simons Gauge Theory: 20 Years After by : Jørgen Ellegaard Andersen
Download or read book Chern-Simons Gauge Theory: 20 Years After written by Jørgen Ellegaard Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
Book Synopsis Mathematical Aspects of Quantum Field Theory by : Edson de Faria
Download or read book Mathematical Aspects of Quantum Field Theory written by Edson de Faria and published by Cambridge University Press. This book was released on 2010-08-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Book Synopsis Hamiltonian Mechanics of Gauge Systems by : Lev V. Prokhorov
Download or read book Hamiltonian Mechanics of Gauge Systems written by Lev V. Prokhorov and published by Cambridge University Press. This book was released on 2011-09-22 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.
Book Synopsis Gauge Theories of the Strong, Weak, and Electromagnetic Interactions by : Chris Quigg
Download or read book Gauge Theories of the Strong, Weak, and Electromagnetic Interactions written by Chris Quigg and published by Princeton University Press. This book was released on 2013-09-22 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This completely revised and updated graduate-level textbook is an ideal introduction to gauge theories and their applications to high-energy particle physics, and takes an in-depth look at two new laws of nature--quantum chromodynamics and the electroweak theory. From quantum electrodynamics through unified theories of the interactions among leptons and quarks, Chris Quigg examines the logic and structure behind gauge theories and the experimental underpinnings of today's theories. Quigg emphasizes how we know what we know, and in the era of the Large Hadron Collider, his insightful survey of the standard model and the next great questions for particle physics makes for compelling reading. The brand-new edition shows how the electroweak theory developed in conversation with experiment. Featuring a wide-ranging treatment of electroweak symmetry breaking, the physics of the Higgs boson, and the importance of the 1-TeV scale, the book moves beyond established knowledge and investigates the path toward unified theories of strong, weak, and electromagnetic interactions. Explicit calculations and diverse exercises allow readers to derive the consequences of these theories. Extensive annotated bibliographies accompany each chapter, amplify points of conceptual or technical interest, introduce further applications, and lead readers to the research literature. Students and seasoned practitioners will profit from the text's current insights, and specialists wishing to understand gauge theories will find the book an ideal reference for self-study. Brand-new edition of a landmark text introducing gauge theories Consistent attention to how we know what we know Explicit calculations develop concepts and engage with experiment Interesting and diverse problems sharpen skills and ideas Extensive annotated bibliographies
Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler
Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
Book Synopsis The Dawning of Gauge Theory by : Lochlainn O'Raifeartaigh
Download or read book The Dawning of Gauge Theory written by Lochlainn O'Raifeartaigh and published by Princeton University Press. This book was released on 2020-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
