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.
Download or read book Future Of Our Physics Including New Frontiers The Proceedings Of The 53rd Course Of The International School Of Subnuclear Physics written by Antonino Zichichi and published by World Scientific. This book was released on 2017-02-13 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this year's Proceedings of the 53rd Course of the International School of Subnuclear Physics is the future of physics, including the new frontiers in other fields.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafał Abłamowicz and published by Springer Science & Business Media. This book was released on 2000 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Download or read book Non associative Structures and Other Related Structures written by Florin Felix Nichita and published by MDPI. This book was released on 2020-06-16 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler (1707–1783) was born in Basel, Switzerland. Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. When its variable is the number pi, Euler's formula evaluates to Euler's identity. On the other hand, the Yang–Baxter equation is considered the most beautiful equation by many scholars. In this book, we study connections between Euler’s formulas and the Yang–Baxter equation. Other interesting sections include: non-associative algebras with metagroup relations; branching functions for admissible representations of affine Lie Algebras; super-Virasoro algebras; dual numbers; UJLA structures; etc.
Download or read book Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes written by Heinrich G W Begehr and published by World Scientific. This book was released on 2003-08-04 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Progress in Analysis written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 2003 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Group Theory written by Pierre Ramond and published by Cambridge University Press. This book was released on 2010-05-13 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac–Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.
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
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.
Download or read book The Road to Reality written by Roger Penrose and published by Vintage. This book was released on 2021-06-09 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: **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
Download or read book Hypercomplex Analysis and Applications written by Irene Sabadini and published by Springer Science & Business Media. This book was released on 2010-12-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Trends in Hypercomplex Analysis written by Swanhild Bernstein and published by Birkhäuser. This book was released on 2016-11-21 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Analytic Automorphic Forms in Hypercomplex Spaces written by Rolf S. Krausshar and published by Springer Science & Business Media. This book was released on 2004-02-23 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Georges Lema tre Life Science and Legacy written by Rodney D. Holder and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2011 marked the 80th anniversary of Georges Lemaître’s primeval atom model of the universe, forerunner of the modern day Big Bang theory. Prompted by this momentous anniversary the Royal Astronomical Society decided to publish a volume of essays on the life, work and faith of this great cosmologist, who was also a Roman Catholic priest. The papers presented in this book examine in detail the historical, cosmological, philosophical and theological issues surrounding the development of the Big Bang theory from its beginnings in the pioneering work of Lemaître through to the modern day. This book offers the best account in English of Lemaître’s life and work. It will be appreciated by professionals and graduate students interested in the history of cosmology.
Download or read book Progress in Physics vol 1 2016 written by Dmitri Rabounski and published by Infinite Study. This book was released on with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
