Beyond Pseudo Rotations In Pseudo Euclidean Spaces

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Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces
  • Author : Abraham Ungar
  • Publisher : Academic Press
  • Release Date : 2018-01-10
  • Total pages : 418
  • ISBN : 9780128117743
  • File Size : 19,9 Mb
  • Total Download : 900
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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

Geometric Science of Information

Geometric Science of Information
  • Author : Frank Nielsen,Frédéric Barbaresco
  • Publisher : Springer
  • Release Date : 2019-08-19
  • Total pages : 770
  • ISBN : 9783030269807
  • File Size : 53,9 Mb
  • Total Download : 764
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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.

A History of Non-Euclidean Geometry

A History of Non-Euclidean Geometry
  • Author : Boris A. Rosenfeld
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-09-08
  • Total pages : 471
  • ISBN : 9781441986801
  • File Size : 54,8 Mb
  • Total Download : 273
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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 of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

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 Date : 2005-11-22
  • Total pages : 528
  • ISBN : 9789814479936
  • File Size : 42,9 Mb
  • Total Download : 739
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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 is devoted to a summary of how relativity theories were born (J Stachel). The second part discusses the most dramatic ramifications of general relativity, such as black holes (P Chrusciel and R Price), space-time singularities (H Nicolai and A Rendall), gravitational waves (P Laguna and P Saulson), the large scale structure of the cosmos (T Padmanabhan); experimental status of this theory (C Will) as well as its practical application to the GPS system (N Ashby). The last part looks beyond Einstein and provides glimpses into what is in store for us in the 21st century. Contributions here include summaries of radical changes in the notions of space and time that are emerging from quantum field theory in curved space-times (Ford), string theory (T Banks), loop quantum gravity (A Ashtekar), quantum cosmology (M Bojowald), discrete approaches (Dowker, Gambini and Pullin) and twistor theory (R Penrose).

Beyond Peaceful Coexistence

Beyond Peaceful Coexistence
  • Author : Licata Ignazio
  • Publisher : World Scientific
  • Release Date : 2016-03-30
  • Total pages : 740
  • ISBN : 9781783268337
  • File Size : 24,5 Mb
  • Total Download : 809
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'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 build new ways of understanding, working and relating to them. The original A. Shimony meaning of the peaceful coexistence (the collapse postulate and non-locality) appear to be just the tip of the iceberg in relation to more serious fundamental issues across physics as a whole.Chapters in this book present perspectives on emergent, discrete, geometrodynamic and topological approaches, as well as a new interpretative spectrum of quantum theories after Copenhagen, discrete time theories, time-less approaches and 'super-fluid' pictures of space-time.As well as stimulating further research among established theoretical physicists, the book can also be used in courses on the philosophy and mathematics of theoretical physics.

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 Date : 2010-03-10
  • Total pages : 255
  • ISBN : 9781439895207
  • File Size : 48,5 Mb
  • Total Download : 224
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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

Singular Integrals in Quantum Euclidean Spaces

Singular Integrals in Quantum Euclidean Spaces
  • Author : Adrían M. González-Pérez,Marius Junge,Javier Parcet
  • Publisher : American Mathematical Society
  • Release Date : 2021-11-16
  • Total pages : 90
  • ISBN : 9781470449377
  • File Size : 38,5 Mb
  • Total Download : 690
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View the abstract.

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 Date : 2019-09-02
  • Total pages : 636
  • ISBN : 9780128147269
  • File Size : 29,5 Mb
  • Total Download : 882
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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 presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications

Variational Approach to Gravity Field Theories

Variational Approach to Gravity Field Theories
  • Author : Alberto Vecchiato
  • Publisher : Springer
  • Release Date : 2017-05-30
  • Total pages : 361
  • ISBN : 9783319512112
  • File Size : 32,6 Mb
  • Total Download : 609
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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 mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughout the text, solved exercises and examples are presented. The book will meet the needs of both students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject.

Special Relativity and How it Works

Special Relativity and How it Works
  • Author : Moses Fayngold
  • Publisher : John Wiley & Sons
  • Release Date : 2008-07-21
  • Total pages : 676
  • ISBN : 3527406077
  • File Size : 40,6 Mb
  • Total Download : 137
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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' (Electromagnetism, Optics, Quantum Mechanics), he not only shows what relativity is, but also how it works. The scope of new material extends to include a chapter on Causality and on Applied Relativity, including astrophysical and accelerator topics. Backed throughout by numerous examples and exercises.

Introduction to Lorentz Geometry

Introduction to Lorentz Geometry
  • Author : Ivo Terek Couto,Alexandre Lymberopoulos
  • Publisher : CRC Press
  • Release Date : 2021-01-05
  • Total pages : 340
  • ISBN : 9781000223347
  • File Size : 23,5 Mb
  • Total Download : 691
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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 provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644

Beyond Einstein

Beyond Einstein
  • Author : David E. Rowe,Tilman Sauer,Scott A. Walter
  • Publisher : Birkhäuser
  • Release Date : 2018-06-18
  • Total pages : 492
  • ISBN : 9781493977086
  • File Size : 29,5 Mb
  • Total Download : 483
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Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

Advanced Particle Physics

Advanced Particle Physics
  • Author : Oleg Boyarkin
  • Publisher : CRC Press
  • Release Date : 2011-02-16
  • Total pages : 568
  • ISBN : 9781439804162
  • File Size : 42,5 Mb
  • Total Download : 272
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Helping readers understand the complicated laws of nature, Advanced Particle Physics Volume II: The Standard Model and Beyond explains the calculations, experimental procedures, and measuring methods of particle physics, particularly quantum chromodynamics (QCD). It also discusses extensions to the Standard Model and the physics of massive neutrinos. Divided into three parts, this volume begins with QCD. It explains the quantization scheme using functional integrals and investigates renormalization problems. The book also calculates cross sections of basic hard processes and covers nonperturbative methods, such as the lattice approach and QCD vacuum. The next part focuses on electroweak interactions, in which the author describes the Glashow–Weinberg–Salam theory and presents composite models and a left-right symmetric model as extensions to the Standard Model. The book concludes with chapters on massive neutrino physics that cover neutrino properties, neutrino oscillation in vacuum and matter, and solar and atmospheric neutrinos.

Advanced Particle Physics Volume II

Advanced Particle Physics Volume II
  • Author : Oleg Boyarkin
  • Publisher : CRC Press
  • Release Date : 2011-02-16
  • Total pages : 565
  • ISBN : 9781439804179
  • File Size : 12,7 Mb
  • Total Download : 283
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Download Advanced Particle Physics Volume II in PDF, Epub, and Kindle

Helping readers understand the complicated laws of nature, Advanced Particle Physics Volume II: The Standard Model and Beyond explains the calculations, experimental procedures, and measuring methods of particle physics, particularly quantum chromodynamics (QCD). It also discusses extensions to the Standard Model and the physics of massive neutrinos. Divided into three parts, this volume begins with QCD. It explains the quantization scheme using functional integrals and investigates renormalization problems. The book also calculates cross sections of basic hard processes and covers nonperturbative methods, such as the lattice approach and QCD vacuum. The next part focuses on electroweak interactions, in which the author describes the Glashow–Weinberg–Salam theory and presents composite models and a left-right symmetric model as extensions to the Standard Model. The book concludes with chapters on massive neutrino physics that cover neutrino properties, neutrino oscillation in vacuum and matter, and solar and atmospheric neutrinos.

CASYS

CASYS
  • Author : Daniel M. Dubois
  • Publisher : Unknown
  • Release Date : 2001
  • Total pages : 438
  • ISBN : 2960026233
  • File Size : 21,5 Mb
  • Total Download : 576
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PDF book entitled CASYS written by Daniel M. Dubois and published by Unknown which was released on 2001 with total hardcover pages 438, the book become popular and critical acclaim.

A Gyrovector Space Approach to Hyperbolic Geometry

A Gyrovector Space Approach to Hyperbolic Geometry
  • Author : Abraham Ungar
  • Publisher : Morgan & Claypool Publishers
  • Release Date : 2009-03-08
  • Total pages : 194
  • ISBN : 9781598298239
  • File Size : 22,7 Mb
  • Total Download : 621
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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 a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry

Précis of Special Relativity

Précis of Special Relativity
  • Author : Olivier Costa de Beauregard
  • Publisher : Unknown
  • Release Date : 1966
  • Total pages : 154
  • ISBN : STANFORD:36105030696806
  • File Size : 20,7 Mb
  • Total Download : 713
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PDF book entitled Précis of Special Relativity written by Olivier Costa de Beauregard and published by Unknown which was released on 1966 with total hardcover pages 154, the book become popular and critical acclaim.

The Worldwide List of Alternative Theories and Critics

The Worldwide List of Alternative Theories and Critics
  • Author : Jean de Climont
  • Publisher : Editions d Assailly
  • Release Date : 2020-11-01
  • Total pages : 2261
  • ISBN : 9782902425174
  • File Size : 44,5 Mb
  • Total Download : 197
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This list (only avalailable in english language) includes scientists involved in scientific fields. The 2021 issue of this directory includes the scientists found in the Internet. The scientists of the directory are only those involved in physics (natural philosophy). The list includes about 10 000 names of scientists (doctors or diplome engineers for more than 70%). Their position is shortly presented together with their proposed alternative theory when applicable. There are more than 2500 authors of such theories, all amazingly very different from one another. Ce répertoire, exclusivement disponible en langue anglaise, inclut les scientifiques, exclusivement dans le domaine de la physique. L'édition 2021 de cette liste comporte près de 10 000 noms de scientifiques, (docteurs ou ingénieurs à plus de 70%). Elle précise leur position de manière succincte et expose, le cas échéant, les lignes directrices de la solution alternative qu'ils proposent. Il y a ainsi plus de 2500 auteurs de telles théories, toutes remarquablement différentes.

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 Date : 2001-11-30
  • Total pages : 402
  • ISBN : 140200351X
  • File Size : 14,7 Mb
  • Total Download : 716
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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 interpretation, and the recent important approach known as “decoherence”. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.

Mathematics and Philosophy

Mathematics and Philosophy
  • Author : Daniel Parrochia
  • Publisher : John Wiley & Sons
  • Release Date : 2018-07-24
  • Total pages : 352
  • ISBN : 9781786302090
  • File Size : 9,6 Mb
  • Total Download : 535
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This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cube, trisection of the angle...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to inspire philosophers (Descartes, Leibniz, Hegel, Husserl, etc.). However, from a certain level of complexity, the mathematicians themselves became philosophers (a movement that begins with Wronsky and Clifford, and continues until Grothendieck).

Advanced Particle Physics Two-Volume Set

Advanced Particle Physics Two-Volume Set
  • Author : Oleg Boyarkin
  • Publisher : Taylor & Francis
  • Release Date : 2011-02-16
  • Total pages : 1224
  • ISBN : 9781439863152
  • File Size : 17,9 Mb
  • Total Download : 809
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Providing a complete foundation to comprehend the physics of the microworld, Advanced Particle Physics, Two-Volume Set develops the models, theoretical framework, and mathematical tools to understand current experiments and make predictions for future experiments. The set brings together a vast array of topics in modern particle physics and distill