A Mathematical Journey To Relativity

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A Mathematical Journey To Relativity

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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date : 2020-06-01

A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.

This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.

A Mathematical Journey To Relativity

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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date : 2024-05-06

A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-06 with Science categories.

The 2nd edition of this textbook features more than 100 pages of new material, including four new chapters, as well as an improved discussion of differential geometry concepts and their applications. The textbook aims to provide a comprehensive geometric description of Special and General Relativity, starting from basic Euclidean geometry to more advanced non-Euclidean geometry and differential geometry. Readers will learn about the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, and the cosmological solutions like de Sitter, Friedman-Lemaître-Robertson-Walker, and Gödel ones, as well as the implications of each of them for the observed physical world. In addition, the book provides step-by-step solutions to problems and exercises, making it an ideal introduction for undergraduate students and readers looking to gain a better understanding of Special and General Relativity. In this new edition, a wide discussion on metric-affine theories of gravity and equivalent formulations of General Relativity is reported. The aim is presenting also topics which could be useful for PhD students and researchers studying General Relativity from an advanced point of view.

A Mathematical Journey To Quantum Mechanics

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Author : Salvatore Capozziello
language : en
Publisher: Springer Nature
Release Date : 2021-09-27

A Mathematical Journey To Quantum Mechanics written by Salvatore Capozziello and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Science categories.

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.

Seven Fundamental Concepts In Spacetime Physics

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Author : Vesselin Petkov
language : en
Publisher: Springer Nature
Release Date : 2024-01-12

Seven Fundamental Concepts In Spacetime Physics written by Vesselin Petkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-12 with Science categories.

The book presents seven fundamental concepts in spacetime physics mostly by following Hermann Minkowski’s revolutionary ideas summarized in his 1908 lecture "Space and Time." These concepts are: spacetime, inertial and accelerated motion in spacetime physics, the origin and nature of inertia in spacetime physics, relativistic mass, gravitation, gravitational waves, and black holes. They have been selected because they appear to be causing most misconceptions and confusion in spacetime physics. This second edition has been revised to include additional clarifications, more detailed elaboration of the arguments and also new material published in the interim.

Relativity A Journey Through Warped Space And Time

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Author : Daniel R. Mayerson
language : en
Publisher: Springer Nature
Release Date : 2019-11-14

Relativity A Journey Through Warped Space And Time written by Daniel R. Mayerson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Science categories.

This primer brilliantly exposes concepts related to special and general relativity for the absolute beginner. It can be used either as an introduction to the subject at a high school level or as a useful compass for undergraduates who want to move the first steps towards Einstein's theories. The book is enhanced throughout with many useful exercises and beautiful illustrations to aid understanding. The topics covered include: Lorentz transformations, length contraction and time dilation, the twin paradox (and other paradoxes), Minkowski spacetime, the Einstein equivalence principle, curvature of space and spacetime, geodesics, parallel transport, Einstein’s equations of general relativity, black holes, wormholes, cosmology, gravitational waves, time machines, and much more.

Noether Symmetries In Theories Of Gravity

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Author : Francesco Bajardi
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-24

Noether Symmetries In Theories Of Gravity written by Francesco Bajardi 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 2022-11-24 with Science categories.

This volume summarizes the many alternatives and extensions to Einstein's General Theory of Relativity, and shows how symmetry principles can be applied to identify physically viable models. The first part of the book establishes the foundations of classical field theory, providing an introduction to symmetry groups and the Noether theorems. A quick overview of general relativity is provided, including discussion of its successes and shortcomings, then several theories of gravity are presented and their main features are summarized. In the second part, the 'Noether Symmetry Approach' is applied to theories of gravity to identify those which contain symmetries. In the third part of the book these selected models are tested through comparison with the latest experiments and observations. This constrains the free parameters in the selected models to fit the current data, demonstrating a useful approach that will allow researchers to construct and constrain modified gravity models for further applications.

Probabilistic Models Of Cosmic Backgrounds

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Author : Anatoliy Malyarenko
language : en
Publisher: CRC Press
Release Date : 2024-06-30

Probabilistic Models Of Cosmic Backgrounds written by Anatoliy Malyarenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-30 with Science categories.

Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.

Mathematical Bridge A An Intuitive Journey In Higher Mathematics 2nd Edition

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Author : Stephen Fletcher Hewson
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-01-20

Mathematical Bridge A An Intuitive Journey In Higher Mathematics 2nd Edition written by Stephen Fletcher Hewson and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-20 with Mathematics categories.

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.

General Relativity Simplified Assessed

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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-08-17

General Relativity Simplified Assessed written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-17 with Science categories.

This book is about the general theory of relativity which is concisely labeled as general relativity. The book is the result of a rather extensive view to the literature of this theory over most of its lifetime reflecting various stages of its development. The book contains 129 solved problems as well as 606 exercises whose detailed solutions are published in another book that accompanies the present book. The book also includes a detailed index and many cross references. The book can be used as an introduction to general relativity at undergraduate and graduate levels. Unlike most other books on general relativity which are mostly dedicated to the presentation, justification, application and validation of the formalism of the theory (and hence rather minor attention is usually paid to the interpretation and epistemology of the theory), this book is primarily interested in the interpretative and epistemological aspects of the theory.

A Mathematical Journey

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Author : Stanley Gudder
language : en
Publisher: McGraw-Hill Companies
Release Date : 1994

A Mathematical Journey written by Stanley Gudder and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.