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Beyond Pseudo Rotations in Pseudo Euclidean Spaces

Beyond Pseudo Rotations in Pseudo Euclidean Spaces
  • Author : Abraham Ungar
  • Publsiher : Academic Press
  • Release : 10 January 2018
  • ISBN : 0128117745
  • Pages : 418 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKBeyond Pseudo Rotations in Pseudo Euclidean Spaces

Summary:
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


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

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Geometric Science of Information

Geometric Science of Information
  • Author : Frank Nielsen,Frédéric Barbaresco
  • Publisher : Springer
  • Release : 19 August 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.

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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

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A Gyrovector Space Approach to Hyperbolic Geometry

A Gyrovector Space Approach to Hyperbolic Geometry
  • Author : Abraham Ungar
  • Publisher : Morgan & Claypool Publishers
  • Release : 08 March 2009
GET THIS BOOKA Gyrovector Space Approach to Hyperbolic Geometry

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to

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Beyond Peaceful Coexistence

Beyond Peaceful Coexistence
  • Author : Licata Ignazio
  • Publisher : World Scientific
  • Release : 30 March 2016
GET THIS BOOKBeyond Peaceful Coexistence

'It may be that a real synthesis of quantum and relativity theories requires not just technical developments but radical conceptual renewal.'J S BellBeyond Peaceful Coexistence: The Emergence of Space, Time and Quantum brings together leading academics in mathematics and physics to address going beyond the 'peaceful coexistence' of space-time descriptions (local and continuous ones) and quantum events (discrete and non-commutative ones). Formidable challenges waiting beyond the Standard Model require a new semantic consistency within the theories in order to

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Group Theory for the Standard Model of Particle Physics and Beyond

Group Theory for the Standard Model of Particle Physics and Beyond
  • Author : Ken J. Barnes
  • Publisher : Taylor & Francis
  • Release : 10 March 2010
GET THIS BOOKGroup Theory for the Standard Model of Particle Physics and Beyond

Based on the author's well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries.After linking symmetries w

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Variational Approach to Gravity Field Theories

Variational Approach to Gravity Field Theories
  • Author : Alberto Vecchiato
  • Publisher : Springer
  • Release : 30 May 2017
GET THIS BOOKVariational Approach to Gravity Field Theories

This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the

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Special Relativity and How it Works

Special Relativity and How it Works
  • Author : Moses Fayngold
  • Publisher : John Wiley & Sons
  • Release : 21 July 2008
GET THIS BOOKSpecial Relativity and How it Works

Based on his successful work "Special Relativity and Motions Faster than Light", Moses Fayngold has written a thorough presentation of the special theory of relativity. The unique feature of the textbook is its two-leveled structure helping students to master the material more effectively: the first level presents a qualitative discussion of a problem, while the second one contains its rigorous treatment. Fayngold points out the connection between fundamental principles and known phenomena. In three new chapters on 'Relativity at Work' (

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Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession
  • Author : Abraham A. Ungar
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKBeyond the Einstein Addition Law and its Gyroscopic Thomas Precession

"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy rogroups and gyrovector spaces, taking the reader to the immensity of hyper bolic geometry that lies beyond the Einstein special theory of

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Riemannian Geometric Statistics in Medical Image Analysis

Riemannian Geometric Statistics in Medical Image Analysis
  • Author : Xavier Pennec,Stefan Sommer,Tom Fletcher
  • Publisher : Academic Press
  • Release : 02 September 2019
GET THIS BOOKRiemannian Geometric Statistics in Medical Image Analysis

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a

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Introduction to Lorentz Geometry

Introduction to Lorentz Geometry
  • Author : Ivo Terek Couto,Alexandre Lymberopoulos
  • Publisher : CRC Press
  • Release : 05 January 2021
GET THIS BOOKIntroduction to Lorentz Geometry

Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to

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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 : 30 November 2001
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

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