Beyond Pseudo Rotations in Pseudo Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas. Introduces the study of generalized gyrogroups and gyrovector spaces Develops new algebraic structures, bi-gyrogroups and bi-gyrovector spaces Helps readers to surmount boundaries between algebra, geometry and physics Assists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric way Generalizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement

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  • Author : Abraham Ungar
  • Publisher : Academic Press
  • Pages : 418 pages
  • ISBN : 0128117745
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKBeyond Pseudo Rotations in Pseudo Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces
  • Author : Abraham Ungar
  • Publisher : Academic Press
  • Release : 10 January 2018
GET THIS BOOKBeyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing

Geometric Science of Information

Geometric Science of Information
  • Author : Frank Nielsen,Frédéric Barbaresco
  • Publisher : Springer
  • Release : 23 September 2019
GET THIS BOOKGeometric Science of Information

This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.

Analytic Hyperbolic Geometry

Analytic Hyperbolic Geometry
  • Author : Abraham A. Ungar
  • Publisher : World Scientific
  • Release : 06 May 2021
GET THIS BOOKAnalytic Hyperbolic Geometry

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed

A History of Non-Euclidean Geometry

A History of Non-Euclidean Geometry
  • Author : Boris A. Rosenfeld
  • Publisher : Springer Science & Business Media
  • Release : 08 September 2012
GET THIS BOOKA History of Non-Euclidean Geometry

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics

The Geometry of Special Relativity

The Geometry of Special Relativity
  • Author : Tevian Dray
  • Publisher : CRC Press
  • Release : 02 July 2012
GET THIS BOOKThe Geometry of Special Relativity

The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them

100 Years Of Relativity: Space-time Structure - Einstein And Beyond

100 Years Of Relativity: Space-time Structure - Einstein And Beyond
  • Author : Abhay Ashtekar
  • Publisher : World Scientific
  • Release : 22 November 2005
GET THIS BOOK100 Years Of Relativity: Space-time Structure - Einstein And Beyond

Thanks to Einstein's relativity theories, our notions of space and time underwent profound revisions about a 100 years ago. The resulting interplay between geometry and physics has dominated all of fundamental physics since then. This volume contains contributions from leading researchers, worldwide, who have thought deeply about the nature and consequences of this interplay. The articles take a long-range view of the subject and distill the most important advances in broad terms, making them easily accessible to non-specialists. The first part

Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds
  • Author : Danny Calegari
  • Publisher : Oxford University Press
  • Release : 17 May 2007
GET THIS BOOKFoliations and the Geometry of 3-Manifolds

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies

Hyperbolic Triangle Centers

Hyperbolic Triangle Centers
  • Author : A.A. Ungar
  • Publisher : Springer Science & Business Media
  • Release : 18 June 2010
GET THIS BOOKHyperbolic Triangle Centers

After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein’s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in

The Landscape of Theoretical Physics: A Global View

The Landscape of Theoretical Physics: A Global View
  • Author : M. Pavsic
  • Publisher : Springer Science & Business Media
  • Release : 11 April 2006
GET THIS BOOKThe Landscape of Theoretical Physics: A Global View

Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett

The General Theory of Relativity

The General Theory of Relativity
  • Author : Anadijiban Das,Andrew DeBenedictis
  • Publisher : Springer Science & Business Media
  • Release : 26 June 2012
GET THIS BOOKThe General Theory of Relativity

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications

Analytic Hyperbolic Geometry in N Dimensions

Analytic Hyperbolic Geometry in N Dimensions
  • Author : Abraham Albert Ungar
  • Publisher : CRC Press
  • Release : 17 December 2014
GET THIS BOOKAnalytic Hyperbolic Geometry in N Dimensions

The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author’s gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her

100 Years of Relativity

100 Years of Relativity
  • Author : Abhay Ashtekar
  • Publisher : World Scientific
  • Release : 06 May 2021
GET THIS BOOK100 Years of Relativity

Divided into three parts, this volume focuses on a summary of how relativity theories were born. It also discusses the ramifications of general relativity, such as black holes, space-time singularities, gravitational waves, the large scale structure of the cosmos, and more. It includes summaries of radical changes in the notions of space and time.