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Author : F. Toppan
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.3/5 (91 download)
Download or read book Exceptional Structures in Mathematics and Physics and the Role of the Octonions written by F. Toppan and published by . This book was released on 2003 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tevian Dray
Publisher : World Scientific
ISBN 13 : 981440182X
Total Pages : 229 pages
Book Rating : 4.8/5 (144 download)
Download or read book The Geometry of the Octonions written by Tevian Dray and published by World Scientific. This book was released on 2015 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.Contents: Introduction"Number Systems: "The Geometry of the Complex NumbersThe Geometry of the QuaternionsThe Geometry of the OctonionsOther Number Systems"Symmetry Groups: "Some Orthogonal GroupsSome Unitary GroupsSome Symplectic GroupsSymmetry Groups over Other Division AlgebrasLie Groups and Lie AlgebrasThe Exceptional Groups"Applications: "Division Algebras in MathematicsOctonionic Eigenvalue ProblemsThe Physics of the OctonionsMagic Squares Readership: Advanced ubdergraduate and graduate students and faculty in mathematics and physics; non-experts with moderately sophisticated mathematics background. Key Features: This book is easily digestible by a large audience wanting to know the elementary introduction to octanionsSuitable for any reader with a grasp of the complex numbers, although familiarity with non-octonionic versions of some of the other topics would be helpfulMany open problems are very accessibleAdvanced topics covered are quite sophisticated, leading up to a clear discussion of (one representation of) the exceptional Lie algebras and their associated root diagrams, and of the octonionic projective spaces on which they act
Author : G.M. Dixon
Publisher : Springer Science & Business Media
ISBN 13 : 1475723156
Total Pages : 242 pages
Book Rating : 4.4/5 (757 download)
Download or read book Division Algebras: written by G.M. Dixon and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: I don't know who Gigerenzer is, but he wrote something very clever that I saw quoted in a popular glossy magazine: "Evolution has tuned the way we think to frequencies of co-occurances, as with the hunter who remembers the area where he has had the most success killing game." This sanguine thought explains my obsession with the division algebras. Every effort I have ever made to connect them to physics - to the design of reality - has succeeded, with my expectations often surpassed. Doubtless this strong statement is colored by a selective memory, but the kind of game I sought, and still seek, seems to frowst about this particular watering hole in droves. I settled down there some years ago and have never feIt like Ieaving. This book is about the beasts I selected for attention (if you will, to ren der this metaphor politically correct, let's say I was a nature photographer), and the kind of tools I had to develop to get the kind of shots Iwanted (the tools that I found there were for my taste overly abstract and theoretical). Half of thisbook is about these tools, and some applications thereof that should demonstrate their power. The rest is devoted to a demonstration of the intimate connection between the mathematics of the division algebras and the Standard Model of quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the connection of this model to lO-dimensional spacetime implied by the mathematics.
Author : Feza Gursey
Publisher : World Scientific
ISBN 13 : 981449822X
Total Pages : 483 pages
Book Rating : 4.8/5 (144 download)
Download or read book On The Role Of Division, Jordan And Related Algebras In Particle Physics written by Feza Gursey and published by World Scientific. This book was released on 1996-11-22 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.
Author : John H. Conway
Publisher : CRC Press
ISBN 13 : 1439864187
Total Pages : 172 pages
Book Rating : 4.4/5 (398 download)
Download or read book On Quaternions and Octonions written by John H. Conway and published by CRC Press. This book was released on 2003-01-23 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 552 pages
Book Rating : 4.8/5 (115 download)
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Author : Ian Stewart
Publisher :
ISBN 13 : 0465082378
Total Pages : 306 pages
Book Rating : 4.4/5 (65 download)
Download or read book Why Beauty Is Truth written by Ian Stewart and published by . This book was released on 2008-04-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics.
Author : J.P Gazeau
Publisher : CRC Press
ISBN 13 : 1482269074
Total Pages : 968 pages
Book Rating : 4.4/5 (822 download)
Download or read book GROUP 24 written by J.P Gazeau and published by CRC Press. This book was released on 2003-11-30 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but a
Author : Feza Grsey
Publisher : World Scientific
ISBN 13 : 9789810228637
Total Pages : 492 pages
Book Rating : 4.2/5 (286 download)
Download or read book On the Role of Division, Jordan and Related Algebras in Particle Physics written by Feza Grsey and published by World Scientific. This book was released on 1996 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.
Author : Tonny A. Springer
Publisher : Springer
ISBN 13 : 3662126222
Total Pages : 212 pages
Book Rating : 4.6/5 (621 download)
Download or read book Octonions, Jordan Algebras and Exceptional Groups written by Tonny A. Springer and published by Springer. This book was released on 2013-12-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.
Author : Lorenzo Magnani
Publisher : Springer
ISBN 13 : 3319305263
Total Pages : 1180 pages
Book Rating : 4.3/5 (193 download)
Download or read book Springer Handbook of Model-Based Science written by Lorenzo Magnani and published by Springer. This book was released on 2017-05-22 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning.
Author : E.M. Rasel
Publisher : IOS Press
ISBN 13 : 1614999376
Total Pages : 432 pages
Book Rating : 4.6/5 (149 download)
Download or read book Foundations of Quantum Theory written by E.M. Rasel and published by IOS Press. This book was released on 2019-01-23 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a summary of the lectures presented at the International School of Physics "Enrico Fermi" on the Foundations of Quantum Theory, organized by the Italian Physical Society in Varenna, Italy from 8-13 July 2016, in collaboration with the Wilhelm und Else Heraeus-Stiftung. It was the first "Enrico Fermi" Summer School on this topic since 1977. Its main goal was to provide an overview of the recent theoretical and experimental developments in an active field of research, the foundations of quantum mechanics. The field is characterized by a dichotomy of unparalleled agreement between theory and experiment on the one hand, and an enormous variety of interpretations of the underlying mathematical formalism on the other hand. This proceedings of the "Enrico Fermi" Summer School of July 2016 contains 21 contributions on a range of topics: the history and interpretations of quantum theory; the principle of complementarity and wave-particle duality; quantum theory from first principles; the reality of the wave function; the concept of the photon; measurement in quantum theory; the interface of quantum theory and general relativity; and quantum optical tests of quantum theory.
Author : Branko Dragović
Publisher :
ISBN 13 :
Total Pages : 580 pages
Book Rating : 4.F/5 ( download)
Download or read book Proceedings of the 2nd Summer School in Modern Mathematical Physics, September 1-12, 2002, Kopaonik, Yugoslavia written by Branko Dragović and published by . This book was released on 2004 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. C. B. Abdalla
Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.:/5 (318 download)
Download or read book Proceedings of the Second International Winter School on Mathematical Methods in Physics written by M. C. B. Abdalla and published by . This book was released on 2003 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Demetrios Bairaktaris
Publisher : AKAKIA Publications
ISBN 13 :
Total Pages : 413 pages
Book Rating : 4.:/5 (661 download)
Download or read book The 8×2n Dimensions of the Particles written by Demetrios Bairaktaris and published by AKAKIA Publications. This book was released on 2021-07-30 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The properties of elementary particles, which determine the interactions between them, must result from the form and function of their internal structure. This investigation stems from the mathematical origin of the concept of particles and the introduction to the process of octal decomposition. It is then established that in order for the complete and specific identification of the dynamic and kinematic characteristics of the function of their internal structures, particles must be defined by a system of 16 dimensions, consisting of two subsystems of eight dimensions.
Author : G.M. Dixon
Publisher : Springer
ISBN 13 : 9781475723168
Total Pages : 238 pages
Book Rating : 4.7/5 (231 download)
Download or read book Division Algebras: written by G.M. Dixon and published by Springer. This book was released on 2013-02-14 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: I don't know who Gigerenzer is, but he wrote something very clever that I saw quoted in a popular glossy magazine: "Evolution has tuned the way we think to frequencies of co-occurances, as with the hunter who remembers the area where he has had the most success killing game." This sanguine thought explains my obsession with the division algebras. Every effort I have ever made to connect them to physics - to the design of reality - has succeeded, with my expectations often surpassed. Doubtless this strong statement is colored by a selective memory, but the kind of game I sought, and still seek, seems to frowst about this particular watering hole in droves. I settled down there some years ago and have never feIt like Ieaving. This book is about the beasts I selected for attention (if you will, to ren der this metaphor politically correct, let's say I was a nature photographer), and the kind of tools I had to develop to get the kind of shots Iwanted (the tools that I found there were for my taste overly abstract and theoretical). Half of thisbook is about these tools, and some applications thereof that should demonstrate their power. The rest is devoted to a demonstration of the intimate connection between the mathematics of the division algebras and the Standard Model of quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the connection of this model to lO-dimensional spacetime implied by the mathematics.
Author : Saul-Paul Sirag
Publisher : World Scientific
ISBN 13 : 9814656518
Total Pages : 276 pages
Book Rating : 4.8/5 (146 download)
Download or read book ADEX Theory written by Saul-Paul Sirag and published by World Scientific. This book was released on 2016-01-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics. Contents:IntroductionThe Octahedral GroupThe Octahedral Double GroupThe McKay CorrespondenceLie Groups and Lie AlgebrasCoxeter''s Reflection GroupsThom–Arnold Catastrophe StructuresALE Spaces and Gravitational InstantonsKnots and Links and BraidsTwistors and ALE SpacesTwo-Dimensional Conformal Field TheoriesElliptic Curves and the Monster GroupSphere Packing and Error-Correcting CodesQubits and Black HolesThe Holographic PrincipleCalabi–Yau Spaces and Mirror SymmetryHeisenberg AlgebrasSummary and OutlookBibliographyGlossaryIndex Readership: Researchers in mathematical physics. Keywords:ADE Graphs;ADE Groups;ADE Lattices;ADE Lie Algebras;ADE Singularities;ADE Catastrophes'
