Groups 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 | : 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 | : Vaughn Climenhaga |
Publisher | : American Mathematical Soc. |
Total Pages | : 442 |
Release | : 2017-04-07 |
Genre | : Mathematics |
ISBN | : 1470434792 |
Download From Groups to Geometry and Back Book in PDF, ePub and Kindle
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Author | : Robert Gilmore |
Publisher | : Cambridge University Press |
Total Pages | : 5 |
Release | : 2008-01-17 |
Genre | : Science |
ISBN | : 113946907X |
Download Lie Groups, Physics, and Geometry Book in PDF, ePub and Kindle
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Author | : P. M. Neumann |
Publisher | : Oxford University Press, USA |
Total Pages | : 268 |
Release | : 1994 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780198534518 |
Download Groups and Geometry Book in PDF, ePub and Kindle
Contains the Oxford Mathematical Institute notes for undergraduate and first-year postgraduates. The first half of the book covers groups, the second half covers geometry and both parts contain a number of exercises.
Author | : D.H. Sattinger |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1475719108 |
Download Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics Book in PDF, ePub and Kindle
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Author | : Pierre Anglès |
Publisher | : Springer Science & Business Media |
Total Pages | : 307 |
Release | : 2007-10-16 |
Genre | : Mathematics |
ISBN | : 0817646434 |
Download Conformal Groups in Geometry and Spin Structures Book in PDF, ePub and Kindle
This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
Author | : Peter Szekeres |
Publisher | : Cambridge University Press |
Total Pages | : 620 |
Release | : 2004-12-16 |
Genre | : Mathematics |
ISBN | : 9780521829601 |
Download A Course in Modern Mathematical Physics Book in PDF, ePub and Kindle
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Author | : Charles Nash |
Publisher | : Courier Corporation |
Total Pages | : 302 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0486318362 |
Download Topology and Geometry for Physicists Book in PDF, ePub and Kindle
Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
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.