Differential Geometry and Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry and Mathematical Physics write by Gerd Rudolph. This book was released on 2012-11-09. Differential Geometry and Mathematical Physics available in PDF, EPUB and Kindle. 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.
Differential Geometry in Physics
Differential Geometry in Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry in Physics write by Gabriel Lugo. This book was released on 2021-10-15. Differential Geometry in Physics available in PDF, EPUB and Kindle. 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.
The Geometry of Physics
The Geometry of Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Physics write by Theodore Frankel. This book was released on 2011-11-03. The Geometry of Physics available in PDF, EPUB and Kindle. 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.
Differential Geometry and Lie Groups for Physicists
Differential Geometry and Lie Groups for Physicists - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry and Lie Groups for Physicists write by Marián Fecko. This book was released on 2006-10-12. Differential Geometry and Lie Groups for Physicists available in PDF, EPUB and Kindle. 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.
Differential Geometry with Applications to Mechanics and Physics
Differential Geometry with Applications to Mechanics and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry with Applications to Mechanics and Physics write by Yves Talpaert. This book was released on 2000-09-12. Differential Geometry with Applications to Mechanics and Physics available in PDF, EPUB and Kindle. An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
