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| fiber bundles in physics: Fibre Bundles D. Husemöller, 2013-06-29 The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gave a coherent treatment of the subject up to that time. About 1955 Milnor gave a construction of a universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal. During the five years from 1950 to 1955, Hirzebruch clarified the notion of characteristic class and used it to prove a general Riemann-Roch theorem for algebraic varieties. This was published in his Ergebnisse Monograph. A systematic development of characteristic classes and their applications to manifolds is given in Part III and is based on the approach of Hirze bruch as modified by Grothendieck. |
| fiber bundles in physics: Fiber Bundle Techniques in Gauge Theories W. Drechsler, M.E. Mayer, 1977-07 |
| fiber bundles in physics: Modern Differential Geometry for Physicists Chris J. Isham, 1999 The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects.Mathematical ReviewsThis book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism. Mathematical Reviews |
| fiber bundles in physics: Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics Steinar Johannesen, 2016-12-08 This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories. |
| fiber bundles in physics: Modelling Critical and Catastrophic Phenomena in Geoscience Pratip Bhattacharyya, Bikas K. Chakrabarti, 2006-09-10 This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or applied mathematics. |
| fiber bundles in physics: The Fiber Bundle Model Alex Hansen, Per Christian Hemmer, Srutarshi Pradhan, 2015-11-02 Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science. The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required. The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics. |
| fiber bundles in physics: The Topology of Fibre Bundles Norman E. Steenrod, 1970 |
| fiber bundles in physics: Differential Geometry and Mathematical Physics Gerd Rudolph, Matthias Schmidt, 2012-11-09 Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact. |
| fiber bundles in physics: Physics from Finance Jakob Schwichtenberg, 2019-02-11 Understanding modern physics doesn’t have to be confusing and hard What if there was an intuitive way to understand how nature fundamentally works? What if there was a book that allowed you to see the whole picture and not just tiny parts of it? Thoughts like this are the reason that Physics from Finance now exists. What will you learn from this book? Get to know all fundamental interactions —Grasp how we can describe electromagnetic interactions, weak interactions, strong interactions and gravity using the same key ideas.Learn how to describe modern physics mathematically — Understand the meaning and origin of the Einstein equation, Maxwell’s equations, and the Schrödinger equation.Develop an intuitive understanding of key concepts — Read how we can understand abstract ideas like Gauge Symmetry, Internal Spaces, Gauge Fields, Connections and Curvature using a simple toy model of the financial market.Get an understanding you can be proud of — Learn why fiber bundles and group theory provide a unified framework for all modern theories of physics. Physics from Finance is the most reader-friendly book on the geometry of modern physics ever written. Here’s why. First of all, it's is nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”.Each chapter, each section, and each page focusses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each formula comes from.The book contains no fluff since unnecessary content quickly leads to confusion. Instead, it ruthlessly focusses on the fundamentals and makes sure you’ll understand them in detail. The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook In total, the book contains more than 100 illustrations that help you understand the most important concepts visually.Whenever a concept is used which was already introduced previously, there is a short sidenote that reminds you where it was first introduced and often recites the main points. In addition, helpful diagrams make sure you won’t get lost. |
| fiber bundles in physics: Principal Bundles Stephen Bruce Sontz, 2015-04-20 This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material. |
| fiber bundles in physics: Lecture Notes on Elementary Topology and Geometry I.M. Singer, J.A. Thorpe, 2015-05-28 At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis. |
| fiber bundles in physics: The Topology of Fibre Bundles Norman Steenrod, 2016-06-02 Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike. |
| fiber bundles in physics: Fiber Bundle Techniques in Gauge Theories W. Drechsler, M.E. Mayer, 2014-03-12 |
| fiber bundles in physics: Topology and Geometry for Physics Helmut Eschrig, 2011-02-09 A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation. |
| fiber bundles in physics: Mathematics for Physics , 2017-11-28 This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles. |
| fiber bundles in physics: Differential Geometry, Gauge Theories, and Gravity M. Göckeler, T. Schücker, 1989-07-28 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. |
| fiber bundles in physics: Geometry, Topology and Physics, Second Edition Mikio Nakahara, 2003-06-04 Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics. |
| fiber bundles in physics: The Geometry of Physics Theodore Frankel, 2011-11-03 This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text. |
| fiber bundles in physics: Fiber Bundles and Homotopy Dai Tamaki, 2021 This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. Furthermore, the notion of fibrations, which is one of three important classes of maps in homotopy theory, can be obtained by extracting the most essential properties of fiber bundles. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book. |
| fiber bundles in physics: Quantization, Geometry and Noncommutative Structures in Mathematics and Physics Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, 2017-10-26 This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory. |
| fiber bundles in physics: History of Original Ideas and Basic Discoveries in Particle Physics Harvey B. Newman, Thomas Ypsilantis, 2012-12-06 The International Conference on the History of Original Ideas and Basic Discoveries, held at the Ettore Majorana Centre for Scientific Culture in Erice, Sicily, July 27-August 4, 1994, brought together sixty of the leading scientists including many Nobel Laureates in high energy physics, principal contributors in other fields of physics such as high Tc superconductivity, particle accelerators and detector instrumentation, and thirty-six talented younger physicists selected from candidates throughout the world. The scientific program, including 49 lectures and a discussion session on the Status and Future Directions in High Energy Physics was inspired by the conference theme: The key experimental discoveries and theoretical breakthroughs of the last 50 years, in particle physics and related fields, have led us to a powerful description of matter in terms of three quark and three lepton families and four fundamental interactions. The most recent generation of experiments at e+e- and proton-proton colliders, and corresponding advances in theoretical calculations, have given us remarkably precise determinations of the basic parameters of the electroweak and strong interactions. These developments, while showing the striking internal consistency of the Standard Model, have also sharpened our view of the many unanswered questions which remain for the next generation: the origin and pattern of particle masses and families, the unification of the interactions including gravity, and the relation between the laws of physics and the initial conditions of the universe. |
| fiber bundles in physics: Fiber bundle techniques in gauge theories Wolfgang Drechsler, Meinhard Edwin Mayer, 1977 |
| fiber bundles in physics: Gauge Theory and Variational Principles David Bleecker, 1981 Detailed and self-contained, this text supplements its rigor with intuitive ideas and is geared toward beginning graduate students and advanced undergraduates. Topics include principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition |
| fiber bundles in physics: Differential Geometry for Physicists Bo-Yu Hou, Bo-Yuan Hou, 1997 This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics. |
| fiber bundles in physics: Basic Bundle Theory and K-Cohomology Invariants Dale Husemöller, Michael Joachim, Branislav Jurco, Martin Schottenloher, 2007-12-10 Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role. |
| fiber bundles in physics: Topology and Geometry for Physicists Charles Nash, Siddhartha Sen, 2013-08-16 Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition. |
| fiber bundles in physics: Connections In Classical And Quantum Field Theory Luigi Mangiarotti, Gennadi A Sardanashvily, 2000-04-28 Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry. |
| fiber bundles in physics: Relativity and Geometry Roberto Torretti, 2014-05-20 Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time. |
| fiber bundles in physics: A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics Antonio Sergio Teixeira Pires, 2019-03-21 In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks. |
| fiber bundles in physics: Riemannian Geometry, Fiber Bundles, Kaluza-Klein Theories and All That.... Robert Coquereaux, Arkadiusz Jadczyk, 1988 This book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental. |
| fiber bundles in physics: Loop Spaces, Characteristic Classes and Geometric Quantization Jean-Luc Brylinski, 2009-12-30 This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge. |
| fiber bundles in physics: Classical Topology And Quantum States Aiyalam P Balachandran, Giuseppe Marmo, A Stern, Bo-sture Skagerstam, 1991-05-16 This book is an introduction to the role of topology in the quantization of classical systems. It is also an introduction to topological solitons with special emphasis on Skyrmions. As regards the first aspect, several issues of current interest are dealt with at a reasonably elementary level. Examples are principal fibre bundles and their role in quantum physics, the possibility of spinorial quantum states in a Lagrangian theory based on tensorial variables, and multiply connected configuration spaces and associated quantum phenomena like the QCD q angle and exotic statistics. The ideas are also illustrated by simple examples such as the spinning particle, the charge-monopole system and strings in 3+1 dimensions. The application of these ideas to quantum gravity is another subject treated at an introductory level. An attempt has been made in this book to introduce the reader to the significance of topology for many distinct physical systems such as spinning particles, the charge- monopole system, strings, Skyrmions, QCD and gravity. The book is an outgrowth of lectures given by the authors at various institutions and conferences. |
| fiber bundles in physics: Vector Bundles and Their Applications Glenys Luke, Alexander S. Mishchenko, 2013-03-09 The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics. |
| fiber bundles in physics: Geometrical Methods of Mathematical Physics Bernard F. Schutz, 1980-01-28 For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms. |
| fiber bundles in physics: Differential Forms in Mathematical Physics , 2009-06-17 Differential Forms in Mathematical Physics |
| fiber bundles in physics: Topology and Physics Chen Ning Yang, Mo-Lin Ge, Yang-Hui He, 2019-03-11 Since its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably -- resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences -- finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community. |
| fiber bundles in physics: Gauge Theory for Fiber Bundles Peter W. Michor, 1991 |
| fiber bundles in physics: The Fiber Bundle Model Alex Hansen, Per Christian Hemmer, Srutarshi Pradhan, 2015-08-24 Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science. The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required. The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics. |
| fiber bundles in physics: Differentiable Manifolds Gerardo F. Torres del Castillo, 2020-06-23 This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics. |
| fiber bundles in physics: The Fiber Bundle Ferenc Kun, Alex Hansen, Purusattam Ray, Srutarshi Pradhan, 2022-01-10 |
Fiber bundle - Wikipedia
In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
nLab fiber bundles in physics - ncatlab.org
Mar 27, 2025 · Two aspects of bundles in physics come together in the theory of gauge fields and combine to produce higher fiber bundles: namely we saw above that a gauge field is itself …
Intuitively, why are bundles so important in Physics?
This is called gerbe or 2-bundle: the only way to realize the Yang-Mills field both locally and globally accurately is to consider it as a section of a bundle whose typical fiber is …
Gauge Theories and Fiber Bundles - arXiv.org
After a brief introduction to the concept of gauge invariance and its relationship to determinism in Section 2, we introduce in Chapters 3 and 4 the notion of fibre bundles in the context of a …
What is a Fibre Bundle? A 5 Minute Introduction - Physics Forums
May 22, 2019 · Intuitively speaking, a fibre bundle is space E which 'locally looks like' a product space B×F, but globally may have a different topological structure.
Fiber Bundles - Physics Travel Guide
Oct 28, 2020 · Fiber bundles are the appropriate mathematical tool to describe, for example, the physics around a magnetic monopole or also instanton effects. (This is described very nicely in …
Fiber bundles | Mathematics for Physics
A bundle map (AKA bundle morphism) is a pair of maps \({\Phi_{E}\colon E\rightarrow E^{\prime}}\) and \({\Phi_{M}\colon M\rightarrow M^{\prime}}\) between bundles that map fibers …
Fiber Bundles - 中国科学技术大学
In applications, especially in di erential geometry and in mathematical physics, one need to study bundles whose bers are no longer vector spaces, and thus the transition maps are no longer...
FIBER BUNDLES AND VECTOR BUNDLES - University of …
In lecture I gave some examples of fiber bundles and one example of a non-fiber bundle. As your texts does not cover this material I’m recording formal definitions and some elementary …
Geometry of Space, Time and Other Things - Linas
Fiber Bundles Central to physics: classical mechanics, electrodynamics, quantum field theory, gravitation, superconductivity. It was not always that way! Unified (pseudo-)Riemannian …
Fiber bundle - Wikipedia
In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
nLab fiber bundles in physics - ncatlab.org
Mar 27, 2025 · Two aspects of bundles in physics come together in the theory of gauge fields and combine to produce higher fiber bundles: namely we saw above that a gauge field is itself …
Intuitively, why are bundles so important in Physics?
This is called gerbe or 2-bundle: the only way to realize the Yang-Mills field both locally and globally accurately is to consider it as a section of a bundle whose typical fiber is …
Gauge Theories and Fiber Bundles - arXiv.org
After a brief introduction to the concept of gauge invariance and its relationship to determinism in Section 2, we introduce in Chapters 3 and 4 the notion of fibre bundles in the context of a …
What is a Fibre Bundle? A 5 Minute Introduction - Physics Forums
May 22, 2019 · Intuitively speaking, a fibre bundle is space E which 'locally looks like' a product space B×F, but globally may have a different topological structure.
Fiber Bundles - Physics Travel Guide
Oct 28, 2020 · Fiber bundles are the appropriate mathematical tool to describe, for example, the physics around a magnetic monopole or also instanton effects. (This is described very nicely in …
Fiber bundles | Mathematics for Physics
A bundle map (AKA bundle morphism) is a pair of maps \({\Phi_{E}\colon E\rightarrow E^{\prime}}\) and \({\Phi_{M}\colon M\rightarrow M^{\prime}}\) between bundles that map fibers …
Fiber Bundles - 中国科学技术大学
In applications, especially in di erential geometry and in mathematical physics, one need to study bundles whose bers are no longer vector spaces, and thus the transition maps are no longer...
FIBER BUNDLES AND VECTOR BUNDLES - University of …
In lecture I gave some examples of fiber bundles and one example of a non-fiber bundle. As your texts does not cover this material I’m recording formal definitions and some elementary …
Geometry of Space, Time and Other Things - Linas
Fiber Bundles Central to physics: classical mechanics, electrodynamics, quantum field theory, gravitation, superconductivity. It was not always that way! Unified (pseudo-)Riemannian …
