On The Role Of Division Jordan And Related Algebras In Particle Physics
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On The Role Of Division Jordan And Related Algebras In Particle Physics
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Author : Feza Grsey
language : en
Publisher: World Scientific
Release Date : 1996
On The Role Of Division Jordan And Related Algebras In Particle Physics written by Feza Grsey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
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.
The Geometry Of The Octonions
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Author : Tevian Dray
language : en
Publisher: World Scientific
Release Date : 2015-04-08
The Geometry Of The Octonions written by Tevian Dray and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-08 with Mathematics categories.
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.
Lie Theory And Its Applications In Physics
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Author : Vladimir Dobrev
language : en
Publisher: Springer Nature
Release Date : 2020-10-15
Lie Theory And Its Applications In Physics written by Vladimir Dobrev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Science categories.
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.
Hypercomplex Analysis And Applications
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Author : Irene Sabadini
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-20
Hypercomplex Analysis And Applications written by Irene Sabadini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-20 with Mathematics categories.
The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis. The list of contributors includes first rate mathematicians and young researchers working on several different aspects in quaternionic and Clifford analysis. Besides original research papers, there are papers providing the state-of-the-art of a specific topic, sometimes containing interdisciplinary fields. The intended audience includes researchers, PhD students, postgraduate students who are interested in the field and in possible connection between hypercomplex analysis and other disciplines, including mathematical analysis, mathematical physics, algebra.
Modern Trends In Hypercomplex Analysis
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Author : Swanhild Bernstein
language : en
Publisher: Birkhäuser
Release Date : 2016-11-21
Modern Trends In Hypercomplex Analysis written by Swanhild Bernstein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.
The Road To Reality
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Author : Roger Penrose
language : en
Publisher: Vintage
Release Date : 2021-06-09
The Road To Reality written by Roger Penrose and has been published by Vintage this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-09 with Science categories.
**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin
Generalized Analytic Automorphic Forms In Hypercomplex Spaces
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Author : Rolf S. Krausshar
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-23
Generalized Analytic Automorphic Forms In Hypercomplex Spaces written by Rolf S. Krausshar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-23 with Mathematics categories.
This book offers basic theory on hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. Vector- and Clifford algebra-valued Eisenstein and Poincaré series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. It establishes explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series, and introduces hypercomplex multiplication of lattices.
Progress In Analysis
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Author : Heinrich G. W. Begehr
language : en
Publisher: World Scientific
Release Date : 2003
Progress In Analysis written by Heinrich G. W. Begehr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes
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Author : Heinrich G W Begehr
language : en
Publisher: World Scientific
Release Date : 2003-08-04
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes written by Heinrich G W Begehr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-04 with Mathematics categories.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Progress In Analysis
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Author : International Society for Analysis, Applications, and Computation. Congress
language : en
Publisher: World Scientific
Release Date : 2003-01-01
Progress In Analysis written by International Society for Analysis, Applications, and Computation. Congress and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics."