Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics

Author : Steinar Johannesen
Publisher : CRC Press
Page : 400 pages
File Size : 53,9 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9781315342627

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Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

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.

Author : Steinar Johannesen
Publisher : CRC Press
Page : 652 pages
File Size : 42,5 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9781498796729

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Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

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.

Author : Norman Earl Steenrod
Publisher : Unknown
Page : 248 pages
File Size : 48,5 Mb
Release : 1951
Category : Fiber bundles (Mathematics)
ISBN : UOM:39015021492148

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The Topology of Fibre Bundles by Norman Earl Steenrod Pdf

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.

Author : Jet Nestruev
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 45,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227399

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Smooth Manifolds and Observables by Jet Nestruev Pdf

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.

Author : Reinhold A. Bertlmann
Publisher : Oxford University Press
Page : 590 pages
File Size : 55,9 Mb
Release : 2000-11-02
Category : Science
ISBN : 0198507623

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Anomalies in Quantum Field Theory by Reinhold A. Bertlmann Pdf

This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations

Author : W. Drechsler,M.E. Mayer
Publisher : Springer
Page : 262 pages
File Size : 47,9 Mb
Release : 1977-07
Category : Mathematics
ISBN : STANFORD:36105005259846

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Fiber Bundle Techniques in Gauge Theories by W. Drechsler,M.E. Mayer Pdf

Author : Norman Steenrod
Publisher : Princeton University Press
Page : 240 pages
File Size : 55,7 Mb
Release : 1999-04-25
Category : Mathematics
ISBN : 9780691005485

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The Topology of Fibre Bundles by Norman Steenrod Pdf

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.

Author : Vagn Lundsgaard Hansen
Publisher : World Scientific
Page : 303 pages
File Size : 41,9 Mb
Release : 2019-11-07
Category : Mathematics
ISBN : 9789811209420

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Fundamental Concepts In Modern Analysis: An Introduction To Nonlinear Analysis (Second Edition) by Vagn Lundsgaard Hansen Pdf

Many applied mathematical disciplines, such as dynamical systems and optimization theory as well as classical mathematical disciplines like differential geometry and the theory of Lie groups, have a common foundation in general topology and multivariate calculus in normed vector spaces. In this book, students from both pure and applied subjects are offered an opportunity to work seriously with fundamental notions from mathematical analysis that are important not only from a mathematical point of view but also occur frequently in the theoretical parts of, for example, the engineering sciences. The book provides complete proofs of the basic results from topology and differentiability of mappings in normed vector spaces. It is a useful resource for students and researchers in mathematics and the many sciences that depend on fundamental techniques from mathematical analysis.In this second edition, the notions of compactness and sequentially compactness are developed with independent proofs for the main results. Thereby the material on compactness is apt for direct applications also in functional analysis, where the notion of sequentially compactness prevails. This edition also covers a new section on partial derivatives, and new material has been incorporated to make a more complete account of higher order derivatives in Banach spaces, including full proofs for symmetry of higher order derivatives and Taylor's formula. The exercise material has been reorganized from a collection of problem sets at the end of the book to a section at the end of each chapter with further results. Readers will find numerous new exercises at different levels of difficulty for practice.

Author : Daniel S. Freed,Sergei Gukov,Ciprian Manolescu,Constantin Teleman,Ulrike Tillmann
Publisher : American Mathematical Society, IAS/Park City Mathematics Institute
Page : 476 pages
File Size : 55,7 Mb
Release : 2021-12-02
Category : Mathematics
ISBN : 9781470461232

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Quantum Field Theory and Manifold Invariants by Daniel S. Freed,Sergei Gukov,Ciprian Manolescu,Constantin Teleman,Ulrike Tillmann Pdf

This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9789814475952

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Topological Library by Anonim Pdf

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 52,8 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

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Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

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.

Author : L.A. Cordero,C.T. Dodson,Manuel de León
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400912656

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Differential Geometry of Frame Bundles by L.A. Cordero,C.T. Dodson,Manuel de León Pdf

It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chillese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : W. D. Curtis,F. R. Miller
Publisher : Unknown
Page : 394 pages
File Size : 41,9 Mb
Release : 1986-05-21
Category : Differentiable manifolds
ISBN : 0122002318

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Differential Manifolds and Theoretical Physics by W. D. Curtis,F. R. Miller Pdf

This work shows how the concepts of manifold theory can be used to describe the physical world. The concepts of modern differential geometry are presented in this comprehensive study of classical mechanics, field theory, and simple quantum effects.

Author : P. D. Sommers
Publisher : Pitman Publishing
Page : 262 pages
File Size : 44,5 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015049070900

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Complex Manifold Techniques in Theoretical Physics by P. D. Sommers Pdf

Author : Torsten Asselmeyer-Maluga,Carl Henry Brans
Publisher : World Scientific
Page : 339 pages
File Size : 55,7 Mb
Release : 2007
Category : Science
ISBN : 9789810241957

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Exotic Smoothness and Physics by Torsten Asselmeyer-Maluga,Carl Henry Brans Pdf

Many Christians have an easier time being saved by grace than they do living in grace every day. But grace is at the center of the life God calls us to--and reflects the heart of the One who calls.These studies in Grace will help you make the connection between grace as a remote biblical concept and grace as a lifestyle--a reality you experience day in, day out. Through an unfolding study of Psalm 23, you'll learn how God--our Good Shepherd--is for you, how he longs to walk with you through temptation, sorrow, and even deep regret. You'll discover God's desire to make his joy your joy. Throughout, you'll learn how enduring, powerful, and life-affirming God's work in your life can be---and rediscover why it's called amazing grace.Leader's guide included!Grace group sessions are:Living in GraceGrace for RegretsSustaining GraceDelighting in GraceA Legacy of GraceGrace ForeverGrace to Share