Geometry Of Yang Mills Fields
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Geometry Of Yang Mills Fields
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Author :
language : en
Publisher:
Release Date : 1979
Geometry Of Yang Mills Fields written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Algebraic topology categories.
Geometry Of Yang Mills Fields
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Author : Michael F. Atiyah
language : en
Publisher: Edizioni della Normale
Release Date : 1979-10
Geometry Of Yang Mills Fields written by Michael F. Atiyah and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-10 with Mathematics categories.
These Lecture Notes are an expanded version of the Fermi Lectures I gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978. In all cases I was addressing a mixed audience of mathematicians and physicists and the presentation had to be tailored accordingly. Throughout, I presented the mathematical material in a somewhat unorthodox order, following a pattern which I felt would relate the new techniques to familiar ground for physicists. The main new results presented in the lectures, namely the construction of all multi-istanton solutions of Yang-Mills fields, is the culmination of several years of fruitful interaction between many physicists and mathematicians. The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his “twistor programme” were ideally suited to the study of the Yang-Mills equations. The instanton problem was then seen to be equivalent to a problem in complex analysis and to one in algebraic geometry. Using the powerful methods of modern algebraic geometry it was not long before the problem was finally solved.
Geometry Of Yang Mills Fields
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Author :
language : it
Publisher:
Release Date : 1995
Geometry Of Yang Mills Fields written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
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.
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.
Twistor Geometry And Field Theory
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Author : R. S. Ward
language : en
Publisher: Cambridge University Press
Release Date : 1990
Twistor Geometry And Field Theory written by R. S. Ward 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 1990 with Mathematics categories.
Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Instanton Counting Quantum Geometry And Algebra
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Author : Taro Kimura
language : en
Publisher: Springer Nature
Release Date : 2021-07-05
Instanton Counting Quantum Geometry And Algebra written by Taro Kimura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Science categories.
This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.
Gauge Fields Knots And Gravity
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Author : John C Baez
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-10-24
Gauge Fields Knots And Gravity written by John C Baez and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-24 with Science categories.
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
The Mathematical Foundations Of Gauge Theories
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Author : Kishore B. Marathe
language : en
Publisher: North Holland
Release Date : 1992
The Mathematical Foundations Of Gauge Theories written by Kishore B. Marathe and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
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.
Michael Atiyah Collected Works
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Author : Michael Atiyah
language : en
Publisher: Oxford University Press
Release Date : 1988-04-28
Michael Atiyah Collected Works written by Michael Atiyah and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-28 with Biography & Autobiography categories.
This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research.