# Search Results for "smooth-manifolds-and-fibre-bundles-with-applications-to-theoretical-physics"

## Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics

**Author**: Steinar Johannesen**Publisher:**CRC Press**ISBN:**1315342626**Category:**Mathematics**Page:**651**View:**8644

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, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics 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.

## Differentiable Manifolds

*A Theoretical Physics Approach*

**Author**: Gerardo F. Torres del Castillo**Publisher:**Springer Science & Business Media**ISBN:**9780817682712**Category:**Mathematics**Page:**275**View:**9814

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.

## Differential Geometry and Mathematical Physics

*Part II. Fibre Bundles, Topology and Gauge Fields*

**Author**: Gerd Rudolph,Matthias Schmidt**Publisher:**Springer**ISBN:**9402409599**Category:**Science**Page:**830**View:**6901

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

## Differential Forms in Mathematical Physics

**Author**: N.A**Publisher:**Elsevier**ISBN:**9780080875248**Category:**Mathematics**Page:**484**View:**1524

Differential Forms in Mathematical Physics

## Differential Geometry for Physicists

**Author**: Bo-Yu Hou,Bo-Yuan Hou**Publisher:**World Scientific Publishing Company**ISBN:**9813105097**Category:**Mathematics**Page:**560**View:**8846

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.

## Topology and Geometry for Physicists

**Author**: Charles Nash,Siddhartha Sen**Publisher:**Courier Corporation**ISBN:**0486318362**Category:**Mathematics**Page:**320**View:**8653

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

## Modern Differential Geometry for Physicists

**Author**: Chris J. Isham**Publisher:**Allied Publishers**ISBN:**9788177643169**Category:**Geometry, Differential**Page:**290**View:**3743

## Fiber Bundle Techniques in Gauge Theories

*Lectures in Mathematical Physics at the University of Texas at Austin*

**Author**: W. Drechsler,M.E. Mayer**Publisher:**Springer**ISBN:**9783662214657**Category:**Science**Page:**251**View:**8966

## Riemannian Geometry, Fiber Bundles, Kaluza-Klein Theories and All That....

**Author**: Robert Coquereaux,Arkadiusz Jadczyk**Publisher:**World Scientific**ISBN:**9789971504267**Category:**Mathematics**Page:**345**View:**754

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.

## Smooth Manifolds and Observables

**Author**: Jet Nestruev**Publisher:**Springer Science & Business Media**ISBN:**0387227393**Category:**Mathematics**Page:**222**View:**3731

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.

## Differential Geometry

*Bundles, Connections, Metrics and Curvature*

**Author**: Clifford Henry Taubes**Publisher:**Oxford University Press**ISBN:**0199605882**Category:**Mathematics**Page:**298**View:**9378

Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.

## Differential Geometric Structures

**Author**: Walter A. Poor**Publisher:**Courier Corporation**ISBN:**0486151913**Category:**Mathematics**Page:**352**View:**5714

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

## Analysis and Algebra on Differentiable Manifolds

*A Workbook for Students and Teachers*

**Author**: Pedro M. Gadea,Jaime Muñoz Masqué,Ihor V. Mykytyuk**Publisher:**Springer Science & Business Media**ISBN:**9400759525**Category:**Mathematics**Page:**618**View:**6061

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

## Physics, Geometry and Topology

**Author**: H.C. Lee**Publisher:**Springer Science & Business Media**ISBN:**1461538025**Category:**Science**Page:**681**View:**2026

The Banff NATO Summer School was held August 14-25, 1989 at the Banff Cen tre, Banff, Albert, Canada. It was a combination of two venues: a summer school in the annual series of Summer School in Theoretical Physics spon sored by the Theoretical Physics Division, Canadian Association of Physi cists, and a NATO Advanced Study Institute. The Organizing Committee for the present school was composed of G. Kunstatter (University of Winnipeg), H.C. Lee (Chalk River Laboratories and University of Western Ontario), R. Kobes (University of Winnipeg), D.l. Toms (University of Newcastle Upon Tyne) and Y.S. Wu (University of Utah). Thanks to the group of lecturers (see Contents) and the timeliness of the courses given, the school, entitled PHYSICS, GEOMETRY AND TOPOLOGY, was popular from the very outset. The number of applications outstripped the 90 places of accommodation reserved at the Banff Centre soon after the school was announced. As the eventual total number of participants was increased to 170, it was still necessary to tum away many deserving applicants. In accordance with the spirit of the school, the geometrical and topologi cal properties in each of the wide ranging topics covered by the lectures were emphasized. A recurring theme in a number of the lectures is the Yang-Baxter relation which characterizes a very large class of integrable systems including: many state models, two-dimensional conformal field theory, quantum field theory and quantum gravity in 2 + I dimensions.

## Topology and Geometry for Physics

**Author**: Helmut Eschrig**Publisher:**Springer**ISBN:**3642147003**Category:**Science**Page:**390**View:**2286

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.

## Applied Differential Geometry

*A Modern Introduction*

**Author**: N.A**Publisher:**World Scientific**ISBN:**9812770720**Category:**Geometry, Differential**Page:**1311**View:**1681

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the worldOCOs leading human motion simulator OCo OC Human Biodynamics EngineOCO, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools OCo this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models."

## Geometry, Topology and Physics, Second Edition

**Author**: Mikio Nakahara**Publisher:**CRC Press**ISBN:**9780750306065**Category:**Mathematics**Page:**596**View:**2011

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.

## Tensors and Manifolds

*With Applications to Physics*

**Author**: Robert Wasserman**Publisher:**Oxford University Press on Demand**ISBN:**9780198510598**Category:**Foreign Language Study**Page:**447**View:**2482

The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics."--Jacket.

## Topology, Geometry, and Gauge Fields

*Foundations*

**Author**: Gregory Naber**Publisher:**Springer Science & Business Media**ISBN:**1475727429**Category:**Mathematics**Page:**396**View:**5298

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

## Geometry of Differential Forms

**Author**: Shigeyuki Morita**Publisher:**American Mathematical Soc.**ISBN:**9780821810453**Category:**Mathematics**Page:**321**View:**4439

Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. This book is a comprehensive introduction to differential forms. It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory. With minimal prerequisites, the book can serve as a textbook for an advanced undergraduate or a graduate course in differential geometry.