Geometry From Isometries To Special Relativity
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Geometry From Isometries To Special Relativity
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Author : Nam-Hoon Lee
language : en
Publisher: Springer Nature
Release Date : 2020-04-28
Geometry From Isometries To Special Relativity written by Nam-Hoon Lee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.
Geometry And Quantum Features Of Special Relativity
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Author : Norbert Dragon
language : en
Publisher: Springer Nature
Release Date : 2025-07-19
Geometry And Quantum Features Of Special Relativity written by Norbert Dragon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-19 with Science categories.
This second edition of "The Geometry of Special Relativity - a Concise Course" offers more than just corrections and enhancements. It includes a new chapter on four-velocities and boosts as points and straight lines of hyperbolic geometry. Quantum properties of relativistic particles are derived from the unitary representations of the Poincaré group. Notably, the massless representation is related to the concept of a Hopf bundle. Scattering theory is developed analogously to the non-relativistic case, relying on proper symmetry postulates. Chapters on quantum fields, reflections of charge, space, and time, and the necessary gauge symmetry of quantized vector fields complete the foundation for evaluating Feynman graphs. An extended appendix covers more than a dozen additional topics. The first half of this edition refines the first edition, using simple diagrams to explain time dilation, length contraction, and Lorentz transformations based on the invariance of the speed of light. The text derives key results of relativistic physics and resolves apparent paradoxes. Following a presentation of the action principle, Noether's theorem, and relativistic mechanics, the book covers the covariant formulation of electrodynamics and classical field theory. The groups of rotations and Lorentz transformations are also examined as a transition to relativistic quantum physics. This text is aimed at graduate students of physics and mathematics seeking an advanced introduction to special relativity and related topics. Its presentation of quantum physics aims to inspire fellow researchers.
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity
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Author : Abraham A. Ungar
language : en
Publisher: World Scientific
Release Date : 2008
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity written by Abraham A. Ungar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami–Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Mצbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincarי ball model of hyperbolic geometry. In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.
Semi Riemannian Geometry With Applications To Relativity
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Author : Barrett O'Neill
language : en
Publisher: Academic Press
Release Date : 1983-07-29
Semi Riemannian Geometry With Applications To Relativity written by Barrett O'Neill and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-07-29 with Mathematics categories.
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
Topics In Geometry
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Author : Robert Bix
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Topics In Geometry written by Robert Bix and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.
The Geometry Of Minkowski Spacetime
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Author : Gregory L. Naber
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
The Geometry Of Minkowski Spacetime written by Gregory L. Naber and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.
A Geometric Algebra Invitation To Space Time Physics Robotics And Molecular Geometry
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Author : Carlile Lavor
language : en
Publisher: Springer
Release Date : 2018-07-12
A Geometric Algebra Invitation To Space Time Physics Robotics And Molecular Geometry written by Carlile Lavor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Mathematics categories.
This book offers a gentle introduction to key elements of Geometric Algebra, along with their applications in Physics, Robotics and Molecular Geometry. Major applications covered are the physics of space-time, including Maxwell electromagnetism and the Dirac equation; robotics, including formulations for the forward and inverse kinematics and an overview of the singularity problem for serial robots; and molecular geometry, with 3D-protein structure calculations using NMR data. The book is primarily intended for graduate students and advanced undergraduates in related fields, but can also benefit professionals in search of a pedagogical presentation of these subjects.
An Introduction To General Relativity
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Author : L. P. Hughston
language : en
Publisher: Cambridge University Press
Release Date : 1990
An Introduction To General Relativity written by L. P. Hughston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.
The Young Carnap S Unknown Master
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Author : Professor Guillermo E Rosado Haddock
language : en
Publisher: Ashgate Publishing, Ltd.
Release Date : 2012-10-01
The Young Carnap S Unknown Master written by Professor Guillermo E Rosado Haddock and has been published by Ashgate Publishing, Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-01 with Philosophy categories.
Examining the scholarly interest of the last two decades in the origins of logical empiricism, and especially the roots of Rudolf Carnap’s Der logische Aufbau der Welt (The Logical Structure of the World), Rosado Haddock challenges the received view, according to which that book should be inserted in the empiricist tradition. In The Young Carnap's Unknown Master Rosado Haddock, builds on the interpretations of Aufbau propounded by Verena Mayer and of Carnap's earlier thesis Der Raum propounded by Sahotra Sarkar and offers instead the most detailed and complete argument on behalf of an Husserlian interpretation of both of these early works of Carnap, as well as offering a refutation of the rival Machian, Kantian, Neo-Kantian, and other more eclectic interpretations of the influences on the work of the young Carnap. The book concludes with an assessment of Quine's critique of Carnap's 'analytic-synthetic' distinction and a criticism of the direction that analytic philosophy has taken in following in the footsteps of Quine's views.
Modern Geometry Methods And Applications
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Author : B.A. Dubrovin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Modern Geometry Methods And Applications written by B.A. Dubrovin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.