Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics Download Ebook PDF Epub Online

Author : Steinar Johannesen
Publisher : CRC Press
Release : 2016-12-08
Page : 641
Category : Mathematics
ISBN 13 : 1498796729
Description :


This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.


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ISBN 13 : 9814475955
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Author : Mahima Ranjan Adhikari
Publisher : Springer
Release : 2016-09-16
Page : 615
Category : Mathematics
ISBN 13 : 813222843X
Description :


This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.


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ISBN 13 : 9814485349
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Author : Terence W Barrett
Dale M Grimes
Publisher : World Scientific
Release : 1995-11-16
Page : 808
Category : Science
ISBN 13 : 9814501085
Description :


Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met. Contents:Foundations:Gauge Theories, and Beyond (R Aldrovandi)Helicity and Electromagnetic Field Topology (G E Marsh)Electromagnetic Gauge as Integration Condition: Einstein's Mass-Energy Equivalence Law and Action-Reaction Opposition (O C de Beauregard)The Symmetry Between Electricity and Magnetism and the Problem of the Existence of a Magnetic Monopole (G Lochak)Quantization as a Wave Effect (P Cornille)Twistors in Field Theory (J Frauendiener & S-T Tsou)Foundational Electrodynamics and Beltrami Vector Fields (D Reed)A Classical Field Theory Explanation of Photons (D M Grimes and C A Grimes)Sagnac Effect: A Consequence of Conservation of Action Due to Gauge Field Global Conformal Invariance in a Multiply-Joined Topology of Coherent Fields (T W Barrett)Gravitation as a Fourth Order Electromagnetic Effect (A K T Assis)Hertzian Invariant Forms of Electromagnetism (T E Phipps Jr)Theory:Pancharatnam's Phase in Polarization Optics (W Dultz & S Klein)Frequency-Dependent Dyadic Green Functions for Bianisotropic Media (W S Weiglhofer)Covariances and Invariances of the Maxwell Postulates (A Lakhtakia)Solitons and Chaos in Periodic Nonlinear Optical Media and Lasers (J-H Feng & F K Kneubühl)The Balance Equations of Energy and Momentum in Classical Electrodynamics (J L Jiménez & I Campos)Non-Abelian Stokes Theorem (B Broda)Extension of Ohm's Law to Electric and Magnetic Dipole Currents (H F Harmuth)Relativistic Implications in Electromagnetic Field Theory (M Sachs)Symmetries, Conservation Laws, and Maxwell's Equations (J Pohjanpelto)Applications:Six Experiments with Magnetic Charge (V F Mikhailov)Ampère Force: Experimental Tests (R Saumont)The Newtonian Electrodynamics and Its Experimental Foundation (P Graneau)Localized Waves and Limited Diffraction Beams (M R Palmer)Analytical and Numerical Methods for Evaluating Electromagnetic Field Integrals Associated with Current-Carrying Wire Antennas (D H Werner)Transmission and Reception of Power by Antennas (D M Grimes & C A Grimes) Readership: Physicists and electrical engineers. keywords:Electromagnetism;A Electromagnetic Fields;A Fields;A Potenials;A Vector Potentials;A Vector;Maxwell Theory;Extended Maxwell Theory;Gauge Fields;Non-Abelian Electromagnetics;Weber;Sagnac Effect;Yang-Mills;Ring Laser Gyro “… it is important to state that Barrett and Grimes have provided a excellent compendium of papers to support the paradigm shift that is occuring and must occur in physical science if we are to accelerate our understanding of the physical world.” Fusion Information Center, Inc.


Author : Linfan Mao
Publisher : Infinite Study
Release : 2011
Page : 484
Category : Combinatorial geometry
ISBN 13 : 159973155X
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Release : 1981-05
Page :
Category : Power resources
ISBN 13 :
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Author : A. Comtet
T. Jolicoeur
Publisher : Springer Science & Business Media
Release : 2000-01-20
Page : 911
Category : Science
ISBN 13 : 3540669094
Description :


Session LXIX. 7 - 31 July 1998


Author : Denis L. Blackmore
Anatoli? Karolevich Prikarpatski?
Publisher : World Scientific
Release : 2011
Page : 542
Category : Mathematics
ISBN 13 : 9814327158
Description :


This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.


Author : B.A. Dubrovin
A.T. Fomenko
Publisher : Springer Science & Business Media
Release : 2013-03-14
Page : 464
Category : Mathematics
ISBN 13 : 1468499467
Description :


manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.


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Release : 1975
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Category : Nuclear energy
ISBN 13 :
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Author : Max Karoubi
Publisher : Springer Science & Business Media
Release : 2009-11-27
Page : 316
Category : Mathematics
ISBN 13 : 3540798900
Description :


From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".


Author : Simon R. Eugster
Publisher : Springer
Release : 2015-03-19
Page : 146
Category : Technology & Engineering
ISBN 13 : 3319164953
Description :


This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.


Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
Release : 2010-12-07
Page : 436
Category : Mathematics
ISBN 13 : 9780857291639
Description :


Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.


Author : G.S Hall
J.R Pulham
Publisher : CRC Press
Release : 1996-01-01
Page : 432
Category : Science
ISBN 13 : 9780750304191
Description :


General Relativity provides an unusually broad survey of the current state of this field. Chapters on mathematical relativity cover many topics, including initial value problems, a new approach to the partial differential equations of physics, and work on exact solutions. The chapters on relativistic cosmology and black holes explore cosmology. Other chapters deal with gravitational waves, experimental relativity, quantum gravity, and aspects of computing in relativity. The book will be useful both to postgraduates and to established workers in the field.


Author : Arno Bohm
Ali Mostafazadeh
Publisher : Springer Science & Business Media
Release : 2013-11-11
Page : 427
Category : Science
ISBN 13 : 3662103338
Description :


From the reviews: "...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).


Author : Stephen T. Lovett
Publisher : CRC Press
Release : 2010-06-11
Page : 440
Category : Mathematics
ISBN 13 : 1439865469
Description :


From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra. Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.


Author : Linfan Mao
Publisher : Infinite Study
Release : 2011
Page : 383
Category : Automorphisms
ISBN 13 : 1599731541
Description :



Author : Mark J.D. Hamilton
Publisher : Springer
Release : 2017-12-06
Page : 658
Category : Mathematics
ISBN 13 : 3319684396
Description :


The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.


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Release : 1997
Page :
Category : Mathematics
ISBN 13 :
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