Differential Geometry And Physics PDF Download
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| Author | : Gerd Rudolph |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 766 |
| Release | : 2012-11-09 |
| Genre | : Science |
| ISBN | : 9400753454 |
Download Differential Geometry and Mathematical Physics Book 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.
| Author | : Gabriel Lugo |
| Publisher | : |
| Total Pages | : 372 |
| Release | : 2021-10-15 |
| Genre | : |
| ISBN | : 9781469669243 |
Download Differential Geometry in Physics Book 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.
| Author | : Theodore Frankel |
| Publisher | : Cambridge University Press |
| Total Pages | : 749 |
| Release | : 2011-11-03 |
| Genre | : Mathematics |
| ISBN | : 1139505610 |
Download The Geometry of Physics Book 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.
| Author | : Yves Talpaert |
| Publisher | : CRC Press |
| Total Pages | : 480 |
| Release | : 2000-09-12 |
| Genre | : Mathematics |
| ISBN | : 9780824703851 |
Download Differential Geometry with Applications to Mechanics and Physics Book 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.
| Author | : Chris J. Isham |
| Publisher | : Allied Publishers |
| Total Pages | : 308 |
| Release | : 2002 |
| Genre | : Geometry, Differential |
| ISBN | : 9788177643169 |
Download Modern Differential Geometry for Physicists Book in PDF, ePub and Kindle
| Author | : Bo-yu Hou |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 561 |
| Release | : 1997-10-31 |
| Genre | : Science |
| ISBN | : 9813105097 |
Download Differential Geometry For Physicists Book in PDF, ePub and Kindle
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 | : Marián Fecko |
| Publisher | : Cambridge University Press |
| Total Pages | : 11 |
| Release | : 2006-10-12 |
| Genre | : Science |
| ISBN | : 1139458035 |
Download Differential Geometry and Lie Groups for Physicists Book 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.
| Author | : Jürgen Jost |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2009-08-17 |
| Genre | : Mathematics |
| ISBN | : 3642005411 |
Download Geometry and Physics Book in PDF, ePub and Kindle
"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 |
| Total Pages | : 397 |
| Release | : 2011-01-26 |
| Genre | : Science |
| ISBN | : 3642147003 |
Download Topology and Geometry for Physics Book in PDF, ePub and Kindle
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.
| Author | : Gerd Rudolph |
| Publisher | : Springer |
| Total Pages | : 830 |
| Release | : 2018-05-09 |
| Genre | : Science |
| ISBN | : 9789402414493 |
Download Differential Geometry and Mathematical Physics Book in PDF, ePub and Kindle
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.
