Clifford Algebras and Spinor Structures

A Special Volume Dedicated to the Memory of Albert Crumeyrolle (1919–1992)

Author: Rafal Ablamowicz,P. Lounesto

Publisher: Springer Science & Business Media

ISBN: 9401584222

Category: Mathematics

Page: 425

View: 6502

This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.
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Clifford (Geometric) Algebras

with applications to physics, mathematics, and engineering

Author: William Baylis

Publisher: Springer Science & Business Media

ISBN: 1461241049

Category: Science

Page: 517

View: 6379

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.
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Clifford (Geometric) Algebras

With Applications in Physics, Mathematics, and Engineering

Author: William E. Baylis

Publisher: Springer Science & Business Media

ISBN: 9780817638689

Category: Mathematics

Page: 517

View: 7869

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.
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Clifford Algebras and Their Application in Mathematical Physics

Aachen 1996

Author: Volker Dietrich,Klaus Habetha,Gerhard Jank

Publisher: Springer Science & Business Media

ISBN: 9401150362

Category: Mathematics

Page: 447

View: 2667

Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics. Audience: This book should appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.
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A Study of Braids

Author: Kunio Murasugi,B. Kurpita

Publisher: Springer Science & Business Media

ISBN: 9780792357674

Category: Computers

Page: 272

View: 6600

This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed. Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids. With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.
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Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations

Author: Constantin Vârsan

Publisher: Kluwer Academic Pub

ISBN: 9780792357186

Category: Mathematics

Page: 238

View: 8227

This book deals mainly with the relevance of integral manifolds associated with a Lie algebra with singularities for studying systems of first order partial differential equations, stochastic differential equations and nonlinear control systems. The analysis is based on the algebraic representation of gradient systems in a Lie algebra, allowing the recovery of the original vector fields and the associated Lie algebra as well. Special attention is paid to nonlinear control systems encompassing specific problems of this theory and their significance for stochastic differential equations. The work is written in a self-contained manner, presupposing only some basic knowledge of algebra, geometry and differential equations. Audience: This volume will be of interest to mathematicians and engineers working in the field of applied geometric and algebraic methods in differential equations. It can also be recommended as a supplementary text for postgraduate students.
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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds

Classical and Quantum Aspects

Author: A.K. Prykarpatsky,I.V. Mykytiuk

Publisher: Springer

ISBN: 9780792350903

Category: Science

Page: 559

View: 6104

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
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Lie groups and Lie algebras

their representations, generalisations, and applications

Author: Boris Petrovich Komrakov

Publisher: Kluwer Academic Pub

ISBN: 9780792349167

Category: Mathematics

Page: 442

View: 8391

This collection brings together papers related to the classical ideas of Sophus Lie. The present work reflects the interests of scientists associated with the International Sophus Lie Center, and provides up-to-date results in Lie groups and Lie algebras, quantum mathematics, hypergroups, homogeneous spaces, Lie superalgebras, the theory of representations and applications to differential equations and integrable systems. Among the topics that are treated are quantization of Poisson structures, applications of multivalued groups, noncommutative aspects of hypergroups, homology invariants of homogeneous spaces, generalisations of the Godbillon-Vey invariant, relations between classical problems of linear analysis and representation theory and the geometry of current groups. Audience: This volume will be of interest to mathematicians and physicists specialising in the theory and applications of Lie groups and Lie algebras, quantum groups, hypergroups and homogeneous spaces.
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Computational and Constructive Design Theory

Author: W. D. Wallis

Publisher: Kluwer Academic Pub

ISBN: N.A

Category: Mathematics

Page: 357

View: 1871

The volume contains eleven papers on various computational techniques used in constructive design theory, written by experts in the field. Included are papers on the use of optimization and numerical analysis techniques, construction of classes of combinatorial design, and attempts to block designs with given small parameters. The volume contains two tutorial papers.
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Operations research and discrete analysis

Author: Alekseĭ D. Korshunov

Publisher: Kluwer Academic Pub

ISBN: N.A

Category: Business & Economics

Page: 331

View: 3168

The contributions to this volume have all been translated from the second volume of the Russian journal Discrete Analysis and Operation Research, published at the Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia. The papers collected here give an excellent overview of recent Russian research in topics such as analysis of algorithms, combinatorics, coding theory, graphs, lower bounds for complexity of Boolean functions and scheduling theory, and can be seen as an update of the book Discrete Analysis and Operational Research, published by Kluwer in 1996.
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Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 6884

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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 7582

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Lectures on Clifford (Geometric) Algebras and Applications

Author: Rafal Ablamowicz,Garret Sobczyk

Publisher: Springer Science & Business Media

ISBN: 0817681906

Category: Mathematics

Page: 221

View: 4136

The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
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