A Mathematical Journey to Relativity PDF Download
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Author: Wladimir-Georges Boskoff
Publisher: Springer Nature
ISBN: 303154823X
Category :
Languages : en
Pages : 556
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Book Description
Author: Wladimir-Georges Boskoff
Publisher: Springer Nature
ISBN: 303154823X
Category :
Languages : en
Pages : 556
Get Book Here
Book Description
Author: Salvatore Capozziello
Publisher: Springer Nature
ISBN: 3030860981
Category : Science
Languages : en
Pages : 294
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Book Description
This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.
Author: Demetrios Christodoulou
Publisher: European Mathematical Society
ISBN: 9783037190050
Category : Science
Languages : en
Pages : 164
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Book Description
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
Author: Stephen Fletcher Hewson
Publisher: World Scientific Publishing Company
ISBN: 9813101245
Category : Mathematics
Languages : en
Pages : 672
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Book Description
Although higher mathematics is beautiful, natural and interconnected, to the uninitiated it can feel like an arbitrary mass of disconnected technical definitions, symbols, theorems and methods. An intellectual gulf needs to be crossed before a true, deep appreciation of mathematics can develop. This book bridges this mathematical gap. It focuses on the process of discovery as much as the content, leading the reader to a clear, intuitive understanding of how and why mathematics exists in the way it does.The narrative does not evolve along traditional subject lines: each topic develops from its simplest, intuitive starting point; complexity develops naturally via questions and extensions. Throughout, the book includes levels of explanation, discussion and passion rarely seen in traditional textbooks. The choice of material is similarly rich, ranging from number theory and the nature of mathematical thought to quantum mechanics and the history of mathematics. It rounds off with a selection of thought-provoking and stimulating exercises for the reader.
Author: Robert M. Wald
Publisher: University of Chicago Press
ISBN: 0226870375
Category : Science
Languages : en
Pages : 507
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Book Description
"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today
Author: Richard A. Mould
Publisher: Springer Science & Business Media
ISBN: 9780387952109
Category : Science
Languages : en
Pages : 476
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Book Description
This comprehensive textbook develops in a logical and coherent way both the formalism and the physical ideas of special and general relativity. Part one focuses on the special theory and begins with the study of relativistic kinematics from three points of view. Part two begins with a chapter introducing differential geometry. Subsequent chapters cover: rotation, the electromagnetic field, and material media. A second chapter on differential geometry provides the background for Einstein's gravitational-field equation and Schwarzschild's solution. The book is aimed at advanced undergraduates and beginning graduate students in physics or astrophysics.
Author: Stephen C. Newman
Publisher: John Wiley & Sons
ISBN: 1119517532
Category : Mathematics
Languages : en
Pages : 656
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Book Description
An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.
Author: James H. Smith
Publisher: Courier Dover Publications
ISBN: 0486808963
Category : Science
Languages : en
Pages : 244
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Book Description
By the year 1900, most of physics seemed to be encompassed in the two great theories of Newtonian mechanics and Maxwell's theory of electromagnetism. Unfortunately, there were inconsistencies between the two theories that seemed irreconcilable. Although many physicists struggled with the problem, it took the genius of Einstein to see that the inconsistencies were concerned not merely with mechanics and electromagnetism, but with our most elementary ideas of space and time. In the special theory of relativity, Einstein resolved these difficulties and profoundly altered our conception of the physical universe. Readers looking for a concise, well-written explanation of one of the most important theories in modern physics need search no further than this lucid undergraduate-level text. Replete with examples that make it especially suitable for self-study, the book assumes only a knowledge of algebra. Topics include classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces, and more.
Author: Éric Gourgoulhon
Publisher: Springer
ISBN: 3642245250
Category : Science
Languages : en
Pages : 304
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Book Description
This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.
Author: Andrew M. Steane
Publisher: Oxford University Press
ISBN: 0199662851
Category : Science
Languages : en
Pages : 436
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Book Description
This book unfolds the subject of Relativity for undergraduate students of physics. It fills a gap between introductory descriptions and texts for researchers. Assuming almost no prior knowledge, it allows the student to handle all the Relativity needed for a university course, with explanations as simple, thorough, and engaging as possible.
