A Geometrical Approach To Physics

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A Geometrical Approach to Physics

Author : DAVID A.. NOBLE BURTON (ADAM.)
Publisher :
ISBN 13 : 9781032133805
Total Pages : 0 pages
Book Rating : 4.1/5 (338 download)

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Book Synopsis A Geometrical Approach to Physics by : DAVID A.. NOBLE BURTON (ADAM.)

Download or read book A Geometrical Approach to Physics written by DAVID A.. NOBLE BURTON (ADAM.) and published by . This book was released on 2024-03-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques. Physical applications are used to develop the techniques and demonstrate their wide-ranging applicability. Formalism is introduced sparingly and step-by-step, where it is needed, and chapters contain exercises for readers to test their understanding. Worked solutions to the exercises are included. It is an ideal textbook for advanced undergraduate or postgraduate courses on mathematical methods for physicists, for students whose background is in physics rather than mathematics. It is assumed that the reader has no prior knowledge of mathematical methods beyond the content of a standard undergraduate physics degree. The purpose of the book is to act as a 'gateway' to more advanced books on the applications of differential geometry in physics. It will also help the reader to better appreciate modern physics research that makes use of differential geometry, and the common features that permeate the discipline as a whole. Key Features: Presents a light and accessible treatment. Can be used as a textbook for a short course on mathematical methods for physicists. Accessible to advanced undergraduates and postgraduates whose background is in physics, not mathematics. David A. Burton received his PhD from Lancaster University, UK, in 2000 and was appointed Lecturer in Physics there in 2005. He is currently Senior Lecturer in Physics at Lancaster. He began his research career in relativistic continuum mechanics and gravitational physics before turning to fluid-structure interactions (in particular, vortex-induced vibration) and, in later years, to relativistic laser-plasma interactions. Adam Noble received his PhD in 2006, also from Lancaster University, and has since held postdoctoral positions at Lancaster and the University of Strathclyde, Scotland, where he is currently a Research Fellow. His interests lie at the interface of physics with geometry, in particular electrodynamics of intense fields, plasma physics and particle physics. The authors maintain a long-standing collaboration and, over the years, have worked on a number of topics connecting electromagnetics, gravitation and plasma physics, including gravitational Sagnac interferometry, relativistic wave-breaking in plasmas, radiation reaction in relativistic plasmas and charged particle beams, and the use of laser-wakefield accelerators in searches for light, weakly-interacting, candidates for dark matter.

A Vector Space Approach to Geometry

Author : Melvin Hausner
Publisher : Courier Dover Publications
ISBN 13 : 0486835391
Total Pages : 417 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis A Vector Space Approach to Geometry by : Melvin Hausner

Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.

A Geometrical Approach to Physics

Author : David A. Burton
Publisher : CRC Press
ISBN 13 : 1003861423
Total Pages : 202 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis A Geometrical Approach to Physics by : David A. Burton

Download or read book A Geometrical Approach to Physics written by David A. Burton and published by CRC Press. This book was released on 2024-03-20 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques. Physical applications are used to develop the techniques and demonstrate their wide-ranging applicability. Formalism is introduced sparingly and step-by-step, where it is needed, and chapters contain exercises for readers to test their understanding. Worked solutions to the exercises are included. It is an ideal textbook for advanced undergraduate or postgraduate courses on mathematical methods for physicists, for students whose background is in physics rather than mathematics. It is assumed that the reader has no prior knowledge of mathematical methods beyond the content of a standard undergraduate physics degree. The purpose of the book is to act as a ‘gateway’ to more advanced books on the applications of differential geometry in physics. It will also help the reader to better appreciate modern physics research that makes use of differential geometry, and the common features that permeate the discipline as a whole. Key Features: Presents a light and accessible treatment Can be used as a textbook for a short course on mathematical methods for physicists Accessible to advanced undergraduates and postgraduates whose background is in physics, not mathematics

General Relativity

Author : Malcolm Ludvigsen
Publisher : Cambridge University Press
ISBN 13 : 9780521639767
Total Pages : 234 pages
Book Rating : 4.6/5 (397 download)

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Book Synopsis General Relativity by : Malcolm Ludvigsen

Download or read book General Relativity written by Malcolm Ludvigsen and published by Cambridge University Press. This book was released on 1999-05-28 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions and hints to selected exercises

An Introduction to Geometrical Physics

Author : Aldrovandi Ruben
Publisher : World Scientific
ISBN 13 : 9813146834
Total Pages : 844 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis An Introduction to Geometrical Physics by : Aldrovandi Ruben

Download or read book An Introduction to Geometrical Physics written by Aldrovandi Ruben and published by World Scientific. This book was released on 2016-10-07 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.

Geometrical Physics in Minkowski Spacetime

Author : E.G.Peter Rowe
Publisher : Springer Science & Business Media
ISBN 13 : 1447138937
Total Pages : 263 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Geometrical Physics in Minkowski Spacetime by : E.G.Peter Rowe

Download or read book Geometrical Physics in Minkowski Spacetime written by E.G.Peter Rowe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This attractive book provides an account of the theory of special relativity from a geometrical viewpoint, explaining the unification and insights that are given by such a treatment. [...] Can be read with profit by all who have taken a first course in relativity physics." ASLIB Book Guide

Geometric Approaches to Quantum Field Theory

Author : Kieran Finn
Publisher : Springer Nature
ISBN 13 : 3030852695
Total Pages : 212 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Geometric Approaches to Quantum Field Theory by : Kieran Finn

Download or read book Geometric Approaches to Quantum Field Theory written by Kieran Finn and published by Springer Nature. This book was released on 2021-10-07 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

Geometrical Vectors

Author : Gabriel Weinreich
Publisher : University of Chicago Press
ISBN 13 : 9780226890487
Total Pages : 132 pages
Book Rating : 4.8/5 (94 download)

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Book Synopsis Geometrical Vectors by : Gabriel Weinreich

Download or read book Geometrical Vectors written by Gabriel Weinreich and published by University of Chicago Press. This book was released on 1998-07-06 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.

A New Approach to Differential Geometry using Clifford's Geometric Algebra

Author : John Snygg
Publisher : Springer Science & Business Media
ISBN 13 : 081768283X
Total Pages : 472 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A New Approach to Differential Geometry using Clifford's Geometric Algebra by : John Snygg

Download or read book A New Approach to Differential Geometry using Clifford's Geometric Algebra written by John Snygg and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Differential Geometry in Physics

Author : Gabriel Lugo
Publisher :
ISBN 13 : 9781469669243
Total Pages : 372 pages
Book Rating : 4.6/5 (692 download)

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Book Synopsis Differential Geometry in Physics by : Gabriel Lugo

Download or read book Differential Geometry in Physics written by Gabriel Lugo and published by . This book was released on 2021-10-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Electrodynamics

Author : William Baylis
Publisher : Springer Science & Business Media
ISBN 13 : 9780817640255
Total Pages : 68 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Electrodynamics by : William Baylis

Download or read book Electrodynamics written by William Baylis and published by Springer Science & Business Media. This book was released on 2004-01-12 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis in this text is on classical electromagnetic theory and electrodynamics, that is, dynamical solutions to the Lorentz-force and Maxwell's equations. The natural appearance of the Minkowski spacetime metric in the paravector space of Clifford's geometric algebra is used to formulate a covariant treatment in special relativity that seamlessly connects spacetime concepts to the spatial vector treatments common in undergraduate texts. Baylis' geometrical interpretation, using such powerful tools as spinors and projectors, essentially allows a component-free notation and avoids the clutter of indices required in tensorial treatments. The exposition is clear and progresses systematically - from a discussion of electromagnetic units and an explanation of how the SI system can be readily converted to the Gaussian or natural Heaviside-Lorentz systems, to an introduction of geometric algebra and the paravector model of spacetime, and finally, special relativity. Other topics include Maxwell's equation(s), the Lorentz-force law, the Fresnel equations, electromagnetic waves and polarization, wave guides, radiation from accelerating charges and time-dependent currents, the Liénard-Wiechert potentials, and radiation reaction, all of which benefit from the modern relativistic approach. Numerous worked examples and exercises dispersed throughout the text help the reader understand new concepts and facilitate self-study of the material. Each chapter concludes with a set of problems, many with answers. Complete solutions are also available. An excellent feature is the integration of Maple into the text, thereby facilitating difficult calculations. To download accompanying Maple worksheets, please visit http://www.cs.uwindsor.ca/users/b/baylis

Complex Analysis

Author : Steven G. Krantz
Publisher : Cambridge University Press
ISBN 13 : 9780883850350
Total Pages : 252 pages
Book Rating : 4.8/5 (53 download)

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Book Synopsis Complex Analysis by : Steven G. Krantz

Download or read book Complex Analysis written by Steven G. Krantz and published by Cambridge University Press. This book was released on 2004 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced textbook on central topic of pure mathematics.

Relativity and Geometry

Author : Roberto Torretti
Publisher : Elsevier
ISBN 13 : 1483147371
Total Pages : 409 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Relativity and Geometry by : Roberto Torretti

Download or read book Relativity and Geometry written by Roberto Torretti and published by Elsevier. This book was released on 2014-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.

Topology, Geometry, and Gauge Fields

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
ISBN 13 : 1475727429
Total Pages : 410 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory L. Naber

Download or read book Topology, Geometry, and Gauge Fields written by Gregory L. Naber and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Topology and Geometry for Physics

Author : Helmut Eschrig
Publisher : Springer
ISBN 13 : 3642147003
Total Pages : 397 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Topology and Geometry for Physics by : Helmut Eschrig

Download or read book Topology and Geometry for Physics written by Helmut Eschrig and published by Springer. This book was released on 2011-01-26 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Geometric Approach to Differential Forms

Author : David Bachman
Publisher : Springer Science & Business Media
ISBN 13 : 0817683046
Total Pages : 167 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A Geometric Approach to Differential Forms by : David Bachman

Download or read book A Geometric Approach to Differential Forms written by David Bachman and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Geometric Methods in Physics

Author : Piotr Kielanowski
Publisher : Springer Science & Business Media
ISBN 13 : 3034804482
Total Pages : 431 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Geometric Methods in Physics by : Piotr Kielanowski

Download or read book Geometric Methods in Physics written by Piotr Kielanowski and published by Springer Science & Business Media. This book was released on 2012-11-05 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.