Differential Geometry And Physics

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Differential Geometry For Physicists

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Author : Bo-yu Hou
language : en
Publisher: World Scientific Publishing Company
Release Date : 1997-10-31

Differential Geometry For Physicists written by Bo-yu Hou 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 1997-10-31 with Science categories.

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.

Differential Geometry And Mathematical Physics

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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09

Differential Geometry And Mathematical Physics written by Gerd Rudolph and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.

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.

Modern Differential Geometry For Physicists

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Author : Chris J. Isham
language : en
Publisher: Allied Publishers
Release Date : 2002

Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.

Topology And Geometry For Physics

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Author : Helmut Eschrig
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-09

Topology And Geometry For Physics written by Helmut Eschrig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-09 with Science categories.

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.

Introductory Differential Geometry For Physicists

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Author : A Visconti
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-10-09

Introductory Differential Geometry For Physicists written by A Visconti 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 1992-10-09 with categories.

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.

Geometry And Physics

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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-17

Geometry And Physics written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-17 with Mathematics categories.

"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.

Differential Geometry Differential Equations And Mathematical Physics

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Author : Maria Ulan
language : en
Publisher: Springer Nature
Release Date : 2021-02-12

Differential Geometry Differential Equations And Mathematical Physics written by Maria Ulan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-12 with Mathematics categories.

This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

Differential Geometry Gauge Theories And Gravity

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Author : M. Göckeler
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-28

Differential Geometry Gauge Theories And Gravity written by M. Göckeler 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 1989-07-28 with Mathematics categories.

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.

Geometrical Methods Of Mathematical Physics

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Author : Bernard F. Schutz
language : en
Publisher: Cambridge University Press
Release Date : 1980-01-28

Geometrical Methods Of Mathematical Physics written by Bernard F. Schutz 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 1980-01-28 with Science categories.

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.