Quaternions Clifford Algebras And Relativistic Physics
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Quaternions Clifford Algebras And Relativistic Physics
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Author : Patrick R. Girard
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Quaternions Clifford Algebras And Relativistic Physics written by Patrick R. Girard 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 2007-06-25 with Mathematics categories.
The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity.
Clifford Algebras And Spinors
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Author : Pertti Lounesto
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-03
Clifford Algebras And Spinors written by Pertti Lounesto and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-03 with Mathematics categories.
In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The initial chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This book also gives the first comprehensive survey of recent research on Clifford algebras. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the analytic side, Brauer-Wall groups and Witt rings are discussed, and Caucy's integral formula is generalized to higher dimensions.
Clifford Algebra To Geometric Calculus
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Author : David Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 1984
Clifford Algebra To Geometric Calculus written by David Hestenes 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 1984 with Mathematics categories.
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Qcd The Dy Process
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Author : Andrea L—pez de Recalde
language : en
Publisher: Lulu.com
Release Date : 2018-01-03
Qcd The Dy Process written by Andrea L—pez de Recalde and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-03 with Science categories.
Recent experiments seem to be ready to answer the question whether QCD be the correct theory of strong interactions at all scales, or just an effective high-energy line of a yet undiscovered theory. With the upgraded Large Hadron Collider, a proton-proton collision will reach the Center of Mass (CoM) energy of 14 TeV per colliding pair. Perturbative QCD will then be tested with the highest precision. In this realm, the present book begins reviewing QCD with the aim to focus on the Drell-Yan process and the experiments conceived to validate it. In doing this the approach will be exclusively perturbative. Non perturbative techniques, such as lattice QCD, QCD sum rules, or concepts like the MIT bag model will not be discussed.
The Standard Electro Weak Theory 2nd Edition
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Author : Andrea López de Recalde
language : en
Publisher: Lulu.com
Release Date : 2017-03-02
The Standard Electro Weak Theory 2nd Edition written by Andrea López de Recalde and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Science categories.
This book is the natural follow-on of the discussion about Quantum Electro Dynamics (QED), begun with my former manual ''Alkali Atomic spectra'', mainly concerning with the description of the atom structure. The Theory of Fields, and then the whole Standard Model, concern particles in relativistic motion. There an atom is ionized and nuclei and particles are brought to collide at relativistic energies. In order to investigate the dynamics an appropriate model is needed. Particles are represented as fields and those fields are themselves quantized as for second quantization. The definition of the Electro-Weak theory and the concept of symmetry breaking are just the prelude to all the physics behind Supersymmetry and Gravitation, and eventually to the Grand Unification Theories (GUT).
Scalar Vector And Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2018-02-27
Scalar Vector And Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-27 with Mathematics categories.
The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index
Matrix Methods Theory Algorithms And Applications Dedicated To The Memory Of Gene Golub
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Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010-04-05
Matrix Methods Theory Algorithms And Applications Dedicated To The Memory Of Gene Golub written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-05 with Mathematics categories.
Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.
Quaternionic Integral Transforms
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Author : Eckhard Hitzer
language : en
Publisher: Springer Nature
Release Date : 2023-08-08
Quaternionic Integral Transforms written by Eckhard Hitzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-08 with Mathematics categories.
This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Integrable Systems And Algebraic Geometry
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Author : Ron Donagi
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-02
Integrable Systems And Algebraic Geometry written by Ron Donagi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-02 with Mathematics categories.
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2009-07-06
Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Mathematics categories.
When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing