**Author**: Bernard F. Schutz

**Publisher:**Cambridge University Press

**ISBN:**9780521298872

**Category:**Mathematics

**Page:**250

**View:**2812

Skip to content
# Search Results for: geometrical-methods-of-mathematical-physics

**Author**: Bernard F. Schutz

**Publisher:** Cambridge University Press

**ISBN:** 9780521298872

**Category:** Mathematics

**Page:** 250

**View:** 2812

For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.

**Author**: Bernard F. Schutz

**Publisher:** Cambridge University Press

**ISBN:** 1107268141

**Category:** Science

**Page:** N.A

**View:** 6666

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**: Charles Nash,Siddhartha Sen

**Publisher:** Courier Corporation

**ISBN:** 0486318362

**Category:** Mathematics

**Page:** 320

**View:** 7083

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

**Author**: V.I. Arnol'd

**Publisher:** Springer Science & Business Media

**ISBN:** 1475720637

**Category:** Mathematics

**Page:** 520

**View:** 8834

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

**Author**: Jürgen Jost

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642005411

**Category:** Mathematics

**Page:** 217

**View:** 5925

"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**: K. Bleuler,M. Werner

**Publisher:** Springer Science & Business Media

**ISBN:** 9401578095

**Category:** Mathematics

**Page:** 471

**View:** 5648

Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987

**Author**: Mikio Nakahara

**Publisher:** CRC Press

**ISBN:** 9780750306065

**Category:** Mathematics

**Page:** 596

**View:** 2272

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

**Author**: Shigeyuki Morita

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821810453

**Category:** Mathematics

**Page:** 321

**View:** 4370

Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. This book is a comprehensive introduction to differential forms. It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory. With minimal prerequisites, the book can serve as a textbook for an advanced undergraduate or a graduate course in differential geometry.
*Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993*

**Author**: Anne Boutet de Monvel,Vladimir Marchenko

**Publisher:** Springer Science & Business Media

**ISBN:** 9780792339090

**Category:** Science

**Page:** 478

**View:** 9321

Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
*An Introduction*

**Author**: Theodore Frankel

**Publisher:** Cambridge University Press

**ISBN:** 1139505610

**Category:** Mathematics

**Page:** N.A

**View:** 3636

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**: Kurt Bernardo Wolf

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540220398

**Category:** Science

**Page:** 376

**View:** 5688

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
*The Concepts Behind an Elegant Language*

**Author**: Don Koks

**Publisher:** Springer Science & Business Media

**ISBN:** 0387327932

**Category:** Science

**Page:** 539

**View:** 1509

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

**Author**: Bernard Schutz

**Publisher:** Cambridge University Press

**ISBN:** 0521887054

**Category:** Science

**Page:** 393

**View:** 6502

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
*An Introduction for Physicists, Engineers and Chemists*

**Author**: Robert Gilmore

**Publisher:** Cambridge University Press

**ISBN:** 113946907X

**Category:** Science

**Page:** N.A

**View:** 4319

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**: Dariusz Chruscinski,Andrzej Jamiolkowski

**Publisher:** Springer Science & Business Media

**ISBN:** 0817681760

**Category:** Mathematics

**Page:** 337

**View:** 1105

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
*Proceedings of the Conference Held at Aix-en-Provence, September 3-7, 1979 and Salamanca, September 10-14, 1979*

**Author**: P. L. Garcia,A. Perez-Rendon,J. M. Souriau

**Publisher:** Springer

**ISBN:** 3540384057

**Category:** Mathematics

**Page:** 542

**View:** 9467

*With Applications to Physics*

**Author**: Robert Wasserman

**Publisher:** Oxford University Press on Demand

**ISBN:** 9780198510598

**Category:** Foreign Language Study

**Page:** 447

**View:** 3363

The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics."--Jacket.

**Author**: Richard L. Bishop,Samuel I. Goldberg

**Publisher:** Courier Corporation

**ISBN:** 0486139239

**Category:** Mathematics

**Page:** 288

**View:** 8838

DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
*An Introductory Guide to Gravity and General Relativity*

**Author**: Bernard Schutz

**Publisher:** Cambridge University Press

**ISBN:** 1139457349

**Category:** Science

**Page:** N.A

**View:** 5932

This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

**Author**: Michael T. Vaughn

**Publisher:** John Wiley & Sons

**ISBN:** 3527618864

**Category:** Science

**Page:** 543

**View:** 3464

A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as well as linear vector spaces, this book includes a more extensive discussion of group theory than can be found in other current textbooks. The main feature of this textbook is its extensive treatment of geometrical methods as applied to physics. With its introduction of differentiable manifolds and a discussion of vectors and forms on such manifolds as part of a first-year graduate course in mathematical methods, the text allows students to grasp at an early stage the contemporary literature on dynamical systems, solitons and related topological solutions to field equations, gauge theories, gravitational theory, and even string theory. Free solutions manual available for lecturers at www.wiley-vch.de/supplements/.

Full PDF Download Free

Privacy Policy

Copyright © 2018 Download PDF Site — Primer WordPress theme by GoDaddy