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Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 40,5 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169
Author : C. J. Isham
Publisher : World Scientific Publishing Company
Page : 182 pages
File Size : 41,6 Mb
Release : 1989
Category : Electronic books
ISBN : 9971509563
1. Differentiable manifolds -- 2. Lie groups -- 3. Fibre bundles
Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 43,7 Mb
Release : 2006-07-27
Category : Mathematics
ISBN : 9780817644741
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
Author : Marián Fecko
Publisher : Cambridge University Press
Page : 11 pages
File Size : 50,8 Mb
Release : 2006-10-12
Category : Science
ISBN : 9781139458030
Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
Author : Bo-Yu Hou,Bo-Yuan Hou
Publisher : OECD Publishing
Page : 564 pages
File Size : 40,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9810231059
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.
Author : A Visconti
Publisher : World Scientific Publishing Company
Page : 424 pages
File Size : 41,9 Mb
Release : 1992-10-09
Category : Electronic
ISBN : 9789813103887
This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.
Author : Bo-Yu Hou,Bo-Yuan Hou
Publisher : World Scientific Publishing Company
Page : 560 pages
File Size : 43,5 Mb
Release : 1997-10-31
Category : Mathematics
ISBN : 9789813105096
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.
Author : Peter Szekeres
Publisher : Cambridge University Press
Page : 620 pages
File Size : 40,5 Mb
Release : 2004-12-16
Category : Mathematics
ISBN : 0521829607
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Author : Gabriel Lugo
Publisher : Unknown
Page : 372 pages
File Size : 50,5 Mb
Release : 2021-10-15
Category : Electronic
ISBN : 1469669242
Differential Geometry in Physics is a treatment of the mathematical foundations of the theory of general relativity and gauge theory of quantum fields. The material is intended to help bridge the gap that often exists between theoretical physics and applied mathematics. The approach is to carve an optimal path to learning this challenging field by appealing to the much more accessible theory of curves and surfaces. The transition from classical differential geometry as developed by Gauss, Riemann and other giants, to the modern approach, is facilitated by a very intuitive approach that sacrifices some mathematical rigor for the sake of understanding the physics. The book features numerous examples of beautiful curves and surfaces often reflected in nature, plus more advanced computations of trajectory of particles in black holes. Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons. Features of this book: * Chapters 1-4 and chapter 5 comprise the content of a one-semester course taught by the author for many years. * The material in the other chapters has served as the foundation for many master's thesis at University of North Carolina Wilmington for students seeking doctoral degrees. * An open access ebook edition is available at Open UNC (https: //openunc.org) * The book contains over 80 illustrations, including a large array of surfaces related to the theory of soliton waves that does not commonly appear in standard mathematical texts on differential geometry.
Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 272 pages
File Size : 54,5 Mb
Release : 1980-01-28
Category : Science
ISBN : 9781107268142
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Author : Theodore Frankel
Publisher : Cambridge University Press
Page : 749 pages
File Size : 42,5 Mb
Release : 2011-11-03
Category : Mathematics
ISBN : 9781139505611
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.
Author : M. Göckeler,T. Schücker
Publisher : Cambridge University Press
Page : 248 pages
File Size : 50,9 Mb
Release : 1989-07-28
Category : Mathematics
ISBN : 0521378214
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.
Author : Antoine Visconti
Publisher : World Scientific Publishing Company Incorporated
Page : 415 pages
File Size : 42,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9971501864
This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.
Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 53,9 Mb
Release : 2009-08-17
Category : Mathematics
ISBN : 9783642005411
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Author : Helmut Eschrig
Publisher : Springer
Page : 397 pages
File Size : 50,6 Mb
Release : 2011-01-26
Category : Science
ISBN : 9783642147005
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.